From a86962cbfd0321387c920a04188512d0de2f3036 Mon Sep 17 00:00:00 2001
From: KatolaZ <katolaz@yahoo.it>
Date: Mon, 19 Oct 2015 16:30:12 +0100
Subject: First commit of MAMMULT documentation
---
doc/html/mammult_doc.css | 154 +++++++++++
doc/html/mammult_doc.html | 307 +++++++++++++++++++++
doc/html/mammult_doc0x.png | Bin 0 -> 735 bytes
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doc/html/mammult_docch1.html | 57 ++++
doc/html/mammult_docch2.html | 53 ++++
doc/html/mammult_docch3.html | 44 +++
doc/html/mammult_docse1.html | 129 +++++++++
doc/html/mammult_docse2.html | 90 ++++++
doc/html/mammult_docse3.html | 55 ++++
doc/html/mammult_docse4.html | 76 +++++
doc/html/mammult_docse5.html | 47 ++++
doc/html/mammult_docse6.html | 40 +++
doc/html/mammult_docse7.html | 49 ++++
doc/html/mammult_docsu1.html | 91 ++++++
doc/html/mammult_docsu10.html | 97 +++++++
doc/html/mammult_docsu11.html | 48 ++++
doc/html/mammult_docsu12.html | 104 +++++++
doc/html/mammult_docsu13.html | 94 +++++++
doc/html/mammult_docsu14.html | 61 ++++
doc/html/mammult_docsu15.html | 134 +++++++++
doc/html/mammult_docsu16.html | 144 ++++++++++
doc/html/mammult_docsu17.html | 106 +++++++
doc/html/mammult_docsu18.html | 102 +++++++
doc/html/mammult_docsu19.html | 52 ++++
doc/html/mammult_docsu2.html | 86 ++++++
doc/html/mammult_docsu20.html | 115 ++++++++
doc/html/mammult_docsu21.html | 125 +++++++++
doc/html/mammult_docsu22.html | 92 ++++++
doc/html/mammult_docsu23.html | 54 ++++
doc/html/mammult_docsu24.html | 79 ++++++
doc/html/mammult_docsu25.html | 81 ++++++
doc/html/mammult_docsu26.html | 87 ++++++
doc/html/mammult_docsu27.html | 52 ++++
doc/html/mammult_docsu28.html | 96 +++++++
doc/html/mammult_docsu29.html | 100 +++++++
doc/html/mammult_docsu3.html | 87 ++++++
doc/html/mammult_docsu30.html | 100 +++++++
doc/html/mammult_docsu31.html | 62 +++++
doc/html/mammult_docsu32.html | 123 +++++++++
doc/html/mammult_docsu33.html | 233 ++++++++++++++++
doc/html/mammult_docsu34.html | 164 +++++++++++
doc/html/mammult_docsu35.html | 140 ++++++++++
doc/html/mammult_docsu36.html | 56 ++++
doc/html/mammult_docsu37.html | 98 +++++++
doc/html/mammult_docsu38.html | 106 +++++++
doc/html/mammult_docsu39.html | 107 +++++++
doc/html/mammult_docsu4.html | 96 +++++++
doc/html/mammult_docsu40.html | 138 +++++++++
doc/html/mammult_docsu41.html | 61 ++++
doc/html/mammult_docsu42.html | 145 ++++++++++
doc/html/mammult_docsu43.html | 158 +++++++++++
doc/html/mammult_docsu44.html | 163 +++++++++++
doc/html/mammult_docsu45.html | 146 ++++++++++
doc/html/mammult_docsu46.html | 40 +++
doc/html/mammult_docsu47.html | 142 ++++++++++
doc/html/mammult_docsu48.html | 42 +++
doc/html/mammult_docsu49.html | 145 ++++++++++
doc/html/mammult_docsu5.html | 95 +++++++
doc/html/mammult_docsu50.html | 46 +++
doc/html/mammult_docsu51.html | 113 ++++++++
doc/html/mammult_docsu52.html | 148 ++++++++++
doc/html/mammult_docsu53.html | 123 +++++++++
doc/html/mammult_docsu54.html | 39 +++
doc/html/mammult_docsu55.html | 121 ++++++++
doc/html/mammult_docsu56.html | 43 +++
doc/html/mammult_docsu57.html | 112 ++++++++
doc/html/mammult_docsu58.html | 109 ++++++++
doc/html/mammult_docsu59.html | 103 +++++++
doc/html/mammult_docsu6.html | 101 +++++++
doc/html/mammult_docsu7.html | 105 +++++++
doc/html/mammult_docsu8.html | 109 ++++++++
doc/html/mammult_docsu9.html | 97 +++++++
doc/latex/latex/dynamics/Ising/multiplex_ising.tex | 22 ++
.../latex/dynamics/randomwalks/entropyrate2add.tex | 24 ++
.../latex/dynamics/randomwalks/entropyrate2int.tex | 24 ++
.../dynamics/randomwalks/entropyrate2mult.tex | 24 ++
.../latex/dynamics/randomwalks/statdistr2.tex | 24 ++
.../models/correlations/tune_qnn_adaptive.tex | 64 +++++
doc/latex/latex/models/correlations/tune_rho.tex | 45 +++
.../latex/models/growth/nibilab_linear_delay.tex | 67 +++++
.../models/growth/nibilab_linear_delay_mix.tex | 68 +++++
.../latex/models/growth/nibilab_linear_delta.tex | 57 ++++
.../models/growth/nibilab_linear_random_times.tex | 63 +++++
.../latex/models/growth/nibilab_nonlinear.tex | 60 ++++
.../latex/models/growth/node_deg_over_time.tex | 50 ++++
doc/latex/latex/models/nullmodels/model_MDM.tex | 37 +++
doc/latex/latex/models/nullmodels/model_MSM.tex | 38 +++
.../models/nullmodels/model_hypergeometric.tex | 33 +++
.../latex/models/nullmodels/model_layer_growth.tex | 46 +++
.../activity/degs_to_activity_overlap.tex | 29 ++
.../latex/structure/activity/degs_to_binary.tex | 32 +++
.../latex/structure/activity/hamming_dist.tex | 31 +++
.../latex/structure/activity/layer_activity.tex | 25 ++
.../structure/activity/layer_activity_vectors.tex | 27 ++
.../latex/structure/activity/multiplexity.tex | 30 ++
.../latex/structure/activity/node_activity.tex | 25 ++
.../structure/activity/node_activity_vectors.tex | 28 ++
.../structure/activity/node_degree_vectors.tex | 30 ++
.../structure/correlations/compute_pearson.tex | 28 ++
.../latex/structure/correlations/compute_rho.tex | 32 +++
.../latex/structure/correlations/compute_tau.tex | 31 +++
.../latex/structure/correlations/dump_k_q.tex | 42 +++
doc/latex/latex/structure/correlations/fit_knn.tex | 50 ++++
.../structure/correlations/knn_q_from_degrees.tex | 64 +++++
.../structure/correlations/knn_q_from_layers.tex | 80 ++++++
.../latex/structure/correlations/rank_nodes.tex | 19 ++
.../structure/correlations/rank_nodes_thresh.tex | 18 ++
.../structure/correlations/rank_occurrence.tex | 24 ++
.../latex/structure/metrics/aggregate_layers_w.tex | 30 ++
.../latex/structure/metrics/avg_edge_overlap.tex | 42 +++
.../structure/metrics/cartography_from_columns.tex | 35 +++
.../metrics/cartography_from_deg_vectors.tex | 32 +++
.../structure/metrics/cartography_from_layers.tex | 45 +++
doc/latex/latex/structure/metrics/edge_overlap.tex | 36 +++
.../latex/structure/metrics/intersect_layers.tex | 28 ++
.../latex/structure/metrics/overlap_degree.tex | 45 +++
doc/latex/latex/structure/metrics/part_coeff.tex | 43 +++
.../structure/reinforcement/reinforcement.tex | 21 ++
doc/latex/mammult_doc.tex | 265 ++++++++++++++++++
145 files changed, 9130 insertions(+)
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create mode 100644 doc/latex/latex/models/growth/nibilab_linear_random_times.tex
create mode 100644 doc/latex/latex/models/growth/nibilab_nonlinear.tex
create mode 100644 doc/latex/latex/models/growth/node_deg_over_time.tex
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create mode 100644 doc/latex/latex/structure/activity/degs_to_activity_overlap.tex
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create mode 100644 doc/latex/latex/structure/activity/multiplexity.tex
create mode 100644 doc/latex/latex/structure/activity/node_activity.tex
create mode 100644 doc/latex/latex/structure/activity/node_activity_vectors.tex
create mode 100644 doc/latex/latex/structure/activity/node_degree_vectors.tex
create mode 100644 doc/latex/latex/structure/correlations/compute_pearson.tex
create mode 100644 doc/latex/latex/structure/correlations/compute_rho.tex
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create mode 100644 doc/latex/latex/structure/metrics/aggregate_layers_w.tex
create mode 100644 doc/latex/latex/structure/metrics/avg_edge_overlap.tex
create mode 100644 doc/latex/latex/structure/metrics/cartography_from_columns.tex
create mode 100644 doc/latex/latex/structure/metrics/cartography_from_deg_vectors.tex
create mode 100644 doc/latex/latex/structure/metrics/cartography_from_layers.tex
create mode 100644 doc/latex/latex/structure/metrics/edge_overlap.tex
create mode 100644 doc/latex/latex/structure/metrics/intersect_layers.tex
create mode 100644 doc/latex/latex/structure/metrics/overlap_degree.tex
create mode 100644 doc/latex/latex/structure/metrics/part_coeff.tex
create mode 100644 doc/latex/latex/structure/reinforcement/reinforcement.tex
create mode 100644 doc/latex/mammult_doc.tex
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new file mode 100644
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diff --git a/doc/html/mammult_doc.html b/doc/html/mammult_doc.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>MAMMULT: Metrics And Models for MULTilayer networks</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <div class="maketitle">
+
+
+
+
+
+
+
+
+
+
+<h2 class="titleHead">MAMMULT: Metrics And Models for MULTilayer
+networks</h2>
+<div class="author" ></div><br />
+<div class="date" ><span
+class="cmr-12">19th</span><span
+class="cmr-12"> October 2015</span></div>
+
+
+
+ </div>
+
+
+
+ <div class="tableofcontents">
+ <span class="chapterToc" >1 <a
+href="mammult_docch1.html#x2-10001" id="QQ2-2-1">Structural descriptors</a></span>
+<br />  <span class="sectionToc" >1.1 <a
+href="mammult_docse1.html#x3-20001.1" id="QQ2-3-2">Basic node, edge, and layer properties</a></span>
+<br />   <span class="subsectionToc" >1.1.1 <a
+href="mammult_docsu1.html#x4-30001.1.1" id="QQ2-4-3">Node and layer activity</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu2.html#x5-40001.1.1" id="QQ2-5-4"><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_activity.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu3.html#x6-50001.1.1" id="QQ2-6-5"><span
+class="cmtt-10x-x-109">layer</span><span
+class="cmtt-10x-x-109">_activity.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu4.html#x7-60001.1.1" id="QQ2-7-6"><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_activity</span><span
+class="cmtt-10x-x-109">_vectors.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu5.html#x8-70001.1.1" id="QQ2-8-7"><span
+class="cmtt-10x-x-109">layer</span><span
+class="cmtt-10x-x-109">_activity</span><span
+class="cmtt-10x-x-109">_vectors.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu6.html#x9-80001.1.1" id="QQ2-9-8"><span
+class="cmtt-10x-x-109">multiplexity.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu7.html#x10-90001.1.1" id="QQ2-10-9"><span
+class="cmtt-10x-x-109">hamming</span><span
+class="cmtt-10x-x-109">_dist.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu8.html#x11-100001.1.1" id="QQ2-11-10"><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_degree</span><span
+class="cmtt-10x-x-109">_vectors.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu9.html#x12-110001.1.1" id="QQ2-12-11"><span
+class="cmtt-10x-x-109">degs</span><span
+class="cmtt-10x-x-109">_to</span><span
+class="cmtt-10x-x-109">_binary.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu10.html#x13-120001.1.1" id="QQ2-13-12"><span
+class="cmtt-10x-x-109">degs</span><span
+class="cmtt-10x-x-109">_to</span><span
+class="cmtt-10x-x-109">_activity</span><span
+class="cmtt-10x-x-109">_overlap.py</span></a></span>
+<br />   <span class="subsectionToc" >1.1.2 <a
+href="mammult_docsu11.html#x14-130001.1.2" id="QQ2-14-13">Layer aggregation</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu12.html#x15-140001.1.2" id="QQ2-15-14"><span
+class="cmtt-10x-x-109">aggregate</span><span
+class="cmtt-10x-x-109">_layers</span><span
+class="cmtt-10x-x-109">_w.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu13.html#x16-150001.1.2" id="QQ2-16-15"><span
+class="cmtt-10x-x-109">intersect</span><span
+class="cmtt-10x-x-109">_layers.py</span></a></span>
+<br />   <span class="subsectionToc" >1.1.3 <a
+href="mammult_docsu14.html#x17-160001.1.3" id="QQ2-17-16">Node degree, participation coefficient, cartography</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu15.html#x18-170001.1.3" id="QQ2-18-17"><span
+class="cmtt-10x-x-109">overlap</span><span
+class="cmtt-10x-x-109">_degree.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu16.html#x19-180001.1.3" id="QQ2-19-18"><span
+class="cmtt-10x-x-109">cartography</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_layers.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu17.html#x20-190001.1.3" id="QQ2-20-19"><span
+class="cmtt-10x-x-109">cartography</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_deg</span><span
+class="cmtt-10x-x-109">_vectors.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu18.html#x21-200001.1.3" id="QQ2-21-20"><span
+class="cmtt-10x-x-109">cartography</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_columns.py</span></a></span>
+<br />   <span class="subsectionToc" >1.1.4 <a
+href="mammult_docsu19.html#x22-210001.1.4" id="QQ2-22-21">Edge overlap, reinforcement</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu20.html#x23-220001.1.4" id="QQ2-23-22"><span
+class="cmtt-10x-x-109">edge</span><span
+class="cmtt-10x-x-109">_overlap.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu21.html#x24-230001.1.4" id="QQ2-24-23"><span
+class="cmtt-10x-x-109">avg</span><span
+class="cmtt-10x-x-109">_edge</span><span
+class="cmtt-10x-x-109">_overlap.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu22.html#x25-240001.1.4" id="QQ2-25-24"><span
+class="cmtt-10x-x-109">reinforcement.py</span></a></span>
+<br />  <span class="sectionToc" >1.2 <a
+href="mammult_docse2.html#x26-250001.2" id="QQ2-26-25">Inter-layer degree correlations</a></span>
+<br />   <span class="subsectionToc" >1.2.1 <a
+href="mammult_docsu23.html#x27-260001.2.1" id="QQ2-27-26">Node ranking</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu24.html#x28-270001.2.1" id="QQ2-28-27"><span
+class="cmtt-10x-x-109">rank</span><span
+class="cmtt-10x-x-109">_nodes.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu25.html#x29-280001.2.1" id="QQ2-29-28"><span
+class="cmtt-10x-x-109">rank</span><span
+class="cmtt-10x-x-109">_nodes</span><span
+class="cmtt-10x-x-109">_thresh.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu26.html#x30-290001.2.1" id="QQ2-30-29"><span
+class="cmtt-10x-x-109">rank</span><span
+class="cmtt-10x-x-109">_occurrence.py</span></a></span>
+<br />   <span class="subsectionToc" >1.2.2 <a
+href="mammult_docsu27.html#x31-300001.2.2" id="QQ2-31-30">Interlayer degree correlation coefficients</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu28.html#x32-310001.2.2" id="QQ2-32-31"><span
+class="cmtt-10x-x-109">compute</span><span
+class="cmtt-10x-x-109">_pearson.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu29.html#x33-320001.2.2" id="QQ2-33-32"><span
+class="cmtt-10x-x-109">compute</span><span
+class="cmtt-10x-x-109">_rho.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu30.html#x34-330001.2.2" id="QQ2-34-33"><span
+class="cmtt-10x-x-109">compute</span><span
+class="cmtt-10x-x-109">_tau.py</span></a></span>
+<br />   <span class="subsectionToc" >1.2.3 <a
+href="mammult_docsu31.html#x35-340001.2.3" id="QQ2-35-34">Interlayer degree correlation functions</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu32.html#x36-350001.2.3" id="QQ2-36-35"><span
+class="cmtt-10x-x-109">dump</span><span
+class="cmtt-10x-x-109">_k</span><span
+class="cmtt-10x-x-109">_q</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu33.html#x37-360001.2.3" id="QQ2-37-36"><span
+class="cmtt-10x-x-109">knn</span><span
+class="cmtt-10x-x-109">_q</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_layers.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu34.html#x38-370001.2.3" id="QQ2-38-37"><span
+class="cmtt-10x-x-109">knn</span><span
+class="cmtt-10x-x-109">_q</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_degrees.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu35.html#x39-380001.2.3" id="QQ2-39-38"><span
+class="cmtt-10x-x-109">fit</span><span
+class="cmtt-10x-x-109">_knn</span></a></span>
+<br /> <span class="chapterToc" >2 <a
+href="mammult_docch2.html#x40-390002" id="QQ2-40-39">Models of multi-layer networks</a></span>
+<br />  <span class="sectionToc" >2.1 <a
+href="mammult_docse3.html#x41-400002.1" id="QQ2-41-40">Null models</a></span>
+<br />   <span class="subsectionToc" >2.1.1 <a
+href="mammult_docsu36.html#x42-410002.1.1" id="QQ2-42-41">Null-models of node and layer activity</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu37.html#x43-420002.1.1" id="QQ2-43-42"><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_hypergeometric.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu38.html#x44-430002.1.1" id="QQ2-44-43"><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_MDM.py</span></a></span>
+
+
+
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu39.html#x45-440002.1.1" id="QQ2-45-44"><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_MSM.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu40.html#x46-450002.1.1" id="QQ2-46-45"><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_layer</span><span
+class="cmtt-10x-x-109">_growth.py</span></a></span>
+<br />  <span class="sectionToc" >2.2 <a
+href="mammult_docse4.html#x47-460002.2" id="QQ2-47-46">Growing multiplex networks</a></span>
+<br />   <span class="subsectionToc" >2.2.1 <a
+href="mammult_docsu41.html#x48-470002.2.1" id="QQ2-48-47">Linear preferential attachment</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu42.html#x49-480002.2.1" id="QQ2-49-48"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_delta</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu43.html#x50-490002.2.1" id="QQ2-50-49"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_delay</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu44.html#x51-500002.2.1" id="QQ2-51-50"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_delay</span><span
+class="cmtt-10x-x-109">_mix</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu45.html#x52-510002.2.1" id="QQ2-52-51"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_random</span><span
+class="cmtt-10x-x-109">_times</span></a></span>
+<br />   <span class="subsectionToc" >2.2.2 <a
+href="mammult_docsu46.html#x53-520002.2.2" id="QQ2-53-52">Non-linear preferential attachment</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu47.html#x54-530002.2.2" id="QQ2-54-53"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_nonlinear</span></a></span>
+<br />   <span class="subsectionToc" >2.2.3 <a
+href="mammult_docsu48.html#x55-540002.2.3" id="QQ2-55-54">Utilities</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu49.html#x56-550002.2.3" id="QQ2-56-55"><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_deg</span><span
+class="cmtt-10x-x-109">_over</span><span
+class="cmtt-10x-x-109">_time.py</span></a></span>
+<br />  <span class="sectionToc" >2.3 <a
+href="mammult_docse5.html#x57-560002.3" id="QQ2-57-56">Multiplex networks with inter-layer degree correlations</a></span>
+<br />   <span class="subsectionToc" >2.3.1 <a
+href="mammult_docsu50.html#x58-570002.3.1" id="QQ2-58-57">Models based on simulated annealing</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu51.html#x59-580002.3.1" id="QQ2-59-58"><span
+class="cmtt-10x-x-109">tune</span><span
+class="cmtt-10x-x-109">_rho</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu52.html#x60-590002.3.1" id="QQ2-60-59"><span
+class="cmtt-10x-x-109">tune</span><span
+class="cmtt-10x-x-109">_qnn</span><span
+class="cmtt-10x-x-109">_adaptive</span></a></span>
+<br /> <span class="chapterToc" >3 <a
+href="mammult_docch3.html#x61-600003" id="QQ2-61-60">Dynamics on multi-layer networks</a></span>
+<br />  <span class="sectionToc" >3.1 <a
+href="mammult_docse6.html#x62-610003.1" id="QQ2-62-61">Interacting opinions - Multilayer ising model</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu53.html#x63-620003.1" id="QQ2-63-62"><span
+class="cmtt-10x-x-109">multiplex</span><span
+class="cmtt-10x-x-109">_ising</span></a></span>
+<br />  <span class="sectionToc" >3.2 <a
+href="mammult_docse7.html#x64-630003.2" id="QQ2-64-63">Biased random walks</a></span>
+<br />   <span class="subsectionToc" >3.2.1 <a
+href="mammult_docsu54.html#x65-640003.2.1" id="QQ2-65-64">Stationary distribution</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu55.html#x66-650003.2.1" id="QQ2-66-65"><span
+class="cmtt-10x-x-109">statdistr2</span></a></span>
+<br />   <span class="subsectionToc" >3.2.2 <a
+href="mammult_docsu56.html#x67-660003.2.2" id="QQ2-67-66">Entropy rate</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu57.html#x68-670003.2.2" id="QQ2-68-67"><span
+class="cmtt-10x-x-109">entropyrate2add</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu58.html#x69-680003.2.2" id="QQ2-69-68"><span
+class="cmtt-10x-x-109">entropyrate2mult</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu59.html#x70-690003.2.2" id="QQ2-70-69"><span
+class="cmtt-10x-x-109">entropyrate2int</span></a></span>
+ </div>
+
+
+
+
+
+
+
+
+<!--l. 265--><p class="noindent" ><span class="next">[<a
+href="mammult_docch1.html" id="tailmammult_doc" >next</a>]</span>
+</body></html>
+
+
+
+
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--- /dev/null
+++ b/doc/html/mammult_docch1.html
@@ -0,0 +1,57 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1 Structural descriptors</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 125--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse1.html" >next</a>] [<a
+href="mammult_doc.html" >prev</a>] [<a
+href="mammult_doc.html#tailmammult_doc" >prev-tail</a>] [<a
+href="#tailmammult_docch1.html">tail</a>] [<a
+href="mammult_doc.html#mammult_docch1.html" >up</a>] </p></div>
+ <h2 class="chapterHead"><span class="titlemark">Chapter 1</span><br /><a
+ id="x2-10001"></a>Structural descriptors</h2>
+ <div class="sectionTOCS">
+  <span class="sectionToc" >1.1 <a
+href="mammult_docse1.html#x3-20001.1">Basic node, edge, and layer properties</a></span>
+<br />   <span class="subsectionToc" >1.1.1 <a
+href="mammult_docsu1.html#x4-30001.1.1">Node and layer activity</a></span>
+<br />   <span class="subsectionToc" >1.1.2 <a
+href="mammult_docsu11.html#x14-130001.1.2">Layer aggregation</a></span>
+<br />   <span class="subsectionToc" >1.1.3 <a
+href="mammult_docsu14.html#x17-160001.1.3">Node degree, participation coefficient, cartography</a></span>
+<br />   <span class="subsectionToc" >1.1.4 <a
+href="mammult_docsu19.html#x22-210001.1.4">Edge overlap, reinforcement</a></span>
+<br />  <span class="sectionToc" >1.2 <a
+href="mammult_docse2.html#x26-250001.2">Inter-layer degree correlations</a></span>
+<br />   <span class="subsectionToc" >1.2.1 <a
+href="mammult_docsu23.html#x27-260001.2.1">Node ranking</a></span>
+<br />   <span class="subsectionToc" >1.2.2 <a
+href="mammult_docsu27.html#x31-300001.2.2">Interlayer degree correlation coefficients</a></span>
+<br />   <span class="subsectionToc" >1.2.3 <a
+href="mammult_docsu31.html#x35-340001.2.3">Interlayer degree correlation functions</a></span>
+
+
+
+ </div>
+
+
+
+
+ <!--l. 208--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse1.html" >next</a>] [<a
+href="mammult_doc.html" >prev</a>] [<a
+href="mammult_doc.html#tailmammult_doc" >prev-tail</a>] [<a
+href="mammult_docch1.html" >front</a>] [<a
+href="mammult_doc.html#mammult_docch1.html" >up</a>] </p></div>
+<!--l. 208--><p class="indent" > <a
+ id="tailmammult_docch1.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docch2.html b/doc/html/mammult_docch2.html
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--- /dev/null
+++ b/doc/html/mammult_docch2.html
@@ -0,0 +1,53 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>2 Models of multi-layer networks</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 208--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse3.html" >next</a>] [<a
+href="mammult_docsu35.html" >prev</a>] [<a
+href="mammult_docsu35.html#tailmammult_docsu35.html" >prev-tail</a>] [<a
+href="#tailmammult_docch2.html">tail</a>] [<a
+href="mammult_doc.html#mammult_docch2.html" >up</a>] </p></div>
+ <h2 class="chapterHead"><span class="titlemark">Chapter 2</span><br /><a
+ id="x40-390002"></a>Models of multi-layer networks</h2>
+ <div class="sectionTOCS">
+  <span class="sectionToc" >2.1 <a
+href="mammult_docse3.html#x41-400002.1">Null models</a></span>
+<br />   <span class="subsectionToc" >2.1.1 <a
+href="mammult_docsu36.html#x42-410002.1.1">Null-models of node and layer activity</a></span>
+<br />  <span class="sectionToc" >2.2 <a
+href="mammult_docse4.html#x47-460002.2">Growing multiplex networks</a></span>
+<br />   <span class="subsectionToc" >2.2.1 <a
+href="mammult_docsu41.html#x48-470002.2.1">Linear preferential attachment</a></span>
+<br />   <span class="subsectionToc" >2.2.2 <a
+href="mammult_docsu46.html#x53-520002.2.2">Non-linear preferential attachment</a></span>
+<br />   <span class="subsectionToc" >2.2.3 <a
+href="mammult_docsu48.html#x55-540002.2.3">Utilities</a></span>
+<br />  <span class="sectionToc" >2.3 <a
+href="mammult_docse5.html#x57-560002.3">Multiplex networks with inter-layer degree correlations</a></span>
+<br />   <span class="subsectionToc" >2.3.1 <a
+href="mammult_docsu50.html#x58-570002.3.1">Models based on simulated annealing</a></span>
+ </div>
+
+
+
+
+
+ <!--l. 247--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse3.html" >next</a>] [<a
+href="mammult_docsu35.html" >prev</a>] [<a
+href="mammult_docsu35.html#tailmammult_docsu35.html" >prev-tail</a>] [<a
+href="mammult_docch2.html" >front</a>] [<a
+href="mammult_doc.html#mammult_docch2.html" >up</a>] </p></div>
+<!--l. 247--><p class="indent" > <a
+ id="tailmammult_docch2.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docch3.html b/doc/html/mammult_docch3.html
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--- /dev/null
+++ b/doc/html/mammult_docch3.html
@@ -0,0 +1,44 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>3 Dynamics on multi-layer networks</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 247--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse6.html" >next</a>] [<a
+href="mammult_docsu52.html" >prev</a>] [<a
+href="mammult_docsu52.html#tailmammult_docsu52.html" >prev-tail</a>] [<a
+href="#tailmammult_docch3.html">tail</a>] [<a
+href="mammult_doc.html#mammult_docch3.html" >up</a>] </p></div>
+ <h2 class="chapterHead"><span class="titlemark">Chapter 3</span><br /><a
+ id="x61-600003"></a>Dynamics on multi-layer networks</h2>
+ <div class="sectionTOCS">
+  <span class="sectionToc" >3.1 <a
+href="mammult_docse6.html#x62-610003.1">Interacting opinions - Multilayer ising model</a></span>
+<br />  <span class="sectionToc" >3.2 <a
+href="mammult_docse7.html#x64-630003.2">Biased random walks</a></span>
+<br />   <span class="subsectionToc" >3.2.1 <a
+href="mammult_docsu54.html#x65-640003.2.1">Stationary distribution</a></span>
+<br />   <span class="subsectionToc" >3.2.2 <a
+href="mammult_docsu56.html#x67-660003.2.2">Entropy rate</a></span>
+ </div>
+
+
+
+
+ <!--l. 265--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse6.html" >next</a>] [<a
+href="mammult_docsu52.html" >prev</a>] [<a
+href="mammult_docsu52.html#tailmammult_docsu52.html" >prev-tail</a>] [<a
+href="mammult_docch3.html" >front</a>] [<a
+href="mammult_doc.html#mammult_docch3.html" >up</a>] </p></div>
+<!--l. 265--><p class="indent" > <a
+ id="tailmammult_docch3.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docse1.html b/doc/html/mammult_docse1.html
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--- /dev/null
+++ b/doc/html/mammult_docse1.html
@@ -0,0 +1,129 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Basic node, edge, and layer properties</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 127--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu1.html" >next</a>] [<a
+href="mammult_docch1.html" >prev</a>] [<a
+href="mammult_docch1.html#tailmammult_docch1.html" >prev-tail</a>] [<a
+href="#tailmammult_docse1.html">tail</a>] [<a
+href="mammult_docch1.html#mammult_docse1.html" >up</a>] </p></div>
+ <h3 class="sectionHead"><span class="titlemark">1.1 </span> <a
+ id="x3-20001.1"></a>Basic node, edge, and layer properties</h3>
+<!--l. 129--><p class="noindent" >
+ <div class="subsectionTOCS">
+   <span class="subsectionToc" >1.1.1 <a
+href="mammult_docsu1.html#x4-30001.1.1">Node and layer activity</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu2.html#x5-40001.1.1"><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_activity.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu3.html#x6-50001.1.1"><span
+class="cmtt-10x-x-109">layer</span><span
+class="cmtt-10x-x-109">_activity.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu4.html#x7-60001.1.1"><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_activity</span><span
+class="cmtt-10x-x-109">_vectors.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu5.html#x8-70001.1.1"><span
+class="cmtt-10x-x-109">layer</span><span
+class="cmtt-10x-x-109">_activity</span><span
+class="cmtt-10x-x-109">_vectors.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu6.html#x9-80001.1.1"><span
+class="cmtt-10x-x-109">multiplexity.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu7.html#x10-90001.1.1"><span
+class="cmtt-10x-x-109">hamming</span><span
+class="cmtt-10x-x-109">_dist.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu8.html#x11-100001.1.1"><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_degree</span><span
+class="cmtt-10x-x-109">_vectors.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu9.html#x12-110001.1.1"><span
+class="cmtt-10x-x-109">degs</span><span
+class="cmtt-10x-x-109">_to</span><span
+class="cmtt-10x-x-109">_binary.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu10.html#x13-120001.1.1"><span
+class="cmtt-10x-x-109">degs</span><span
+class="cmtt-10x-x-109">_to</span><span
+class="cmtt-10x-x-109">_activity</span><span
+class="cmtt-10x-x-109">_overlap.py</span></a></span>
+<br />   <span class="subsectionToc" >1.1.2 <a
+href="mammult_docsu11.html#x14-130001.1.2">Layer aggregation</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu12.html#x15-140001.1.2"><span
+class="cmtt-10x-x-109">aggregate</span><span
+class="cmtt-10x-x-109">_layers</span><span
+class="cmtt-10x-x-109">_w.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu13.html#x16-150001.1.2"><span
+class="cmtt-10x-x-109">intersect</span><span
+class="cmtt-10x-x-109">_layers.py</span></a></span>
+<br />   <span class="subsectionToc" >1.1.3 <a
+href="mammult_docsu14.html#x17-160001.1.3">Node degree, participation coefficient, cartography</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu15.html#x18-170001.1.3"><span
+class="cmtt-10x-x-109">overlap</span><span
+class="cmtt-10x-x-109">_degree.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu16.html#x19-180001.1.3"><span
+class="cmtt-10x-x-109">cartography</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_layers.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu17.html#x20-190001.1.3"><span
+class="cmtt-10x-x-109">cartography</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_deg</span><span
+class="cmtt-10x-x-109">_vectors.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu18.html#x21-200001.1.3"><span
+class="cmtt-10x-x-109">cartography</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_columns.py</span></a></span>
+<br />   <span class="subsectionToc" >1.1.4 <a
+href="mammult_docsu19.html#x22-210001.1.4">Edge overlap, reinforcement</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu20.html#x23-220001.1.4"><span
+class="cmtt-10x-x-109">edge</span><span
+class="cmtt-10x-x-109">_overlap.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu21.html#x24-230001.1.4"><span
+class="cmtt-10x-x-109">avg</span><span
+class="cmtt-10x-x-109">_edge</span><span
+class="cmtt-10x-x-109">_overlap.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu22.html#x25-240001.1.4"><span
+class="cmtt-10x-x-109">reinforcement.py</span></a></span>
+ </div>
+
+
+
+
+
+
+ <!--l. 172--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu1.html" >next</a>] [<a
+href="mammult_docch1.html" >prev</a>] [<a
+href="mammult_docch1.html#tailmammult_docch1.html" >prev-tail</a>] [<a
+href="mammult_docse1.html" >front</a>] [<a
+href="mammult_docch1.html#mammult_docse1.html" >up</a>] </p></div>
+<!--l. 172--><p class="indent" > <a
+ id="tailmammult_docse1.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docse2.html b/doc/html/mammult_docse2.html
new file mode 100644
index 0000000..deb5077
--- /dev/null
+++ b/doc/html/mammult_docse2.html
@@ -0,0 +1,90 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Inter-layer degree correlations</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 172--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu23.html" >next</a>] [<a
+href="mammult_docsu22.html" >prev</a>] [<a
+href="mammult_docsu22.html#tailmammult_docsu22.html" >prev-tail</a>] [<a
+href="#tailmammult_docse2.html">tail</a>] [<a
+href="mammult_docch1.html#mammult_docse2.html" >up</a>] </p></div>
+ <h3 class="sectionHead"><span class="titlemark">1.2 </span> <a
+ id="x26-250001.2"></a>Inter-layer degree correlations</h3>
+<!--l. 174--><p class="noindent" >
+ <div class="subsectionTOCS">
+   <span class="subsectionToc" >1.2.1 <a
+href="mammult_docsu23.html#x27-260001.2.1">Node ranking</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu24.html#x28-270001.2.1"><span
+class="cmtt-10x-x-109">rank</span><span
+class="cmtt-10x-x-109">_nodes.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu25.html#x29-280001.2.1"><span
+class="cmtt-10x-x-109">rank</span><span
+class="cmtt-10x-x-109">_nodes</span><span
+class="cmtt-10x-x-109">_thresh.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu26.html#x30-290001.2.1"><span
+class="cmtt-10x-x-109">rank</span><span
+class="cmtt-10x-x-109">_occurrence.py</span></a></span>
+<br />   <span class="subsectionToc" >1.2.2 <a
+href="mammult_docsu27.html#x31-300001.2.2">Interlayer degree correlation coefficients</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu28.html#x32-310001.2.2"><span
+class="cmtt-10x-x-109">compute</span><span
+class="cmtt-10x-x-109">_pearson.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu29.html#x33-320001.2.2"><span
+class="cmtt-10x-x-109">compute</span><span
+class="cmtt-10x-x-109">_rho.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu30.html#x34-330001.2.2"><span
+class="cmtt-10x-x-109">compute</span><span
+class="cmtt-10x-x-109">_tau.py</span></a></span>
+<br />   <span class="subsectionToc" >1.2.3 <a
+href="mammult_docsu31.html#x35-340001.2.3">Interlayer degree correlation functions</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu32.html#x36-350001.2.3"><span
+class="cmtt-10x-x-109">dump</span><span
+class="cmtt-10x-x-109">_k</span><span
+class="cmtt-10x-x-109">_q</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu33.html#x37-360001.2.3"><span
+class="cmtt-10x-x-109">knn</span><span
+class="cmtt-10x-x-109">_q</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_layers.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu34.html#x38-370001.2.3"><span
+class="cmtt-10x-x-109">knn</span><span
+class="cmtt-10x-x-109">_q</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_degrees.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu35.html#x39-380001.2.3"><span
+class="cmtt-10x-x-109">fit</span><span
+class="cmtt-10x-x-109">_knn</span></a></span>
+ </div>
+
+
+
+
+
+ <!--l. 208--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu23.html" >next</a>] [<a
+href="mammult_docsu22.html" >prev</a>] [<a
+href="mammult_docsu22.html#tailmammult_docsu22.html" >prev-tail</a>] [<a
+href="mammult_docse2.html" >front</a>] [<a
+href="mammult_docch1.html#mammult_docse2.html" >up</a>] </p></div>
+<!--l. 208--><p class="indent" > <a
+ id="tailmammult_docse2.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docse3.html b/doc/html/mammult_docse3.html
new file mode 100644
index 0000000..f05a21a
--- /dev/null
+++ b/doc/html/mammult_docse3.html
@@ -0,0 +1,55 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Null models</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 210--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu36.html" >next</a>] [<a
+href="mammult_docch2.html" >prev</a>] [<a
+href="mammult_docch2.html#tailmammult_docch2.html" >prev-tail</a>] [<a
+href="#tailmammult_docse3.html">tail</a>] [<a
+href="mammult_docch2.html#mammult_docse3.html" >up</a>] </p></div>
+ <h3 class="sectionHead"><span class="titlemark">2.1 </span> <a
+ id="x41-400002.1"></a>Null models</h3>
+<!--l. 212--><p class="noindent" >
+ <div class="subsectionTOCS">
+   <span class="subsectionToc" >2.1.1 <a
+href="mammult_docsu36.html#x42-410002.1.1">Null-models of node and layer activity</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu37.html#x43-420002.1.1"><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_hypergeometric.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu38.html#x44-430002.1.1"><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_MDM.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu39.html#x45-440002.1.1"><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_MSM.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu40.html#x46-450002.1.1"><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_layer</span><span
+class="cmtt-10x-x-109">_growth.py</span></a></span>
+ </div>
+
+
+
+ <!--l. 220--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu36.html" >next</a>] [<a
+href="mammult_docch2.html" >prev</a>] [<a
+href="mammult_docch2.html#tailmammult_docch2.html" >prev-tail</a>] [<a
+href="mammult_docse3.html" >front</a>] [<a
+href="mammult_docch2.html#mammult_docse3.html" >up</a>] </p></div>
+<!--l. 220--><p class="indent" > <a
+ id="tailmammult_docse3.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docse4.html b/doc/html/mammult_docse4.html
new file mode 100644
index 0000000..2ab68dd
--- /dev/null
+++ b/doc/html/mammult_docse4.html
@@ -0,0 +1,76 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Growing multiplex networks</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 220--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu41.html" >next</a>] [<a
+href="mammult_docsu40.html" >prev</a>] [<a
+href="mammult_docsu40.html#tailmammult_docsu40.html" >prev-tail</a>] [<a
+href="#tailmammult_docse4.html">tail</a>] [<a
+href="mammult_docch2.html#mammult_docse4.html" >up</a>] </p></div>
+ <h3 class="sectionHead"><span class="titlemark">2.2 </span> <a
+ id="x47-460002.2"></a>Growing multiplex networks</h3>
+<!--l. 222--><p class="noindent" >
+ <div class="subsectionTOCS">
+   <span class="subsectionToc" >2.2.1 <a
+href="mammult_docsu41.html#x48-470002.2.1">Linear preferential attachment</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu42.html#x49-480002.2.1"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_delta</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu43.html#x50-490002.2.1"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_delay</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu44.html#x51-500002.2.1"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_delay</span><span
+class="cmtt-10x-x-109">_mix</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu45.html#x52-510002.2.1"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_random</span><span
+class="cmtt-10x-x-109">_times</span></a></span>
+<br />   <span class="subsectionToc" >2.2.2 <a
+href="mammult_docsu46.html#x53-520002.2.2">Non-linear preferential attachment</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu47.html#x54-530002.2.2"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_nonlinear</span></a></span>
+<br />   <span class="subsectionToc" >2.2.3 <a
+href="mammult_docsu48.html#x55-540002.2.3">Utilities</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu49.html#x56-550002.2.3"><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_deg</span><span
+class="cmtt-10x-x-109">_over</span><span
+class="cmtt-10x-x-109">_time.py</span></a></span>
+ </div>
+
+
+
+
+
+ <!--l. 239--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu41.html" >next</a>] [<a
+href="mammult_docsu40.html" >prev</a>] [<a
+href="mammult_docsu40.html#tailmammult_docsu40.html" >prev-tail</a>] [<a
+href="mammult_docse4.html" >front</a>] [<a
+href="mammult_docch2.html#mammult_docse4.html" >up</a>] </p></div>
+<!--l. 239--><p class="indent" > <a
+ id="tailmammult_docse4.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docse5.html b/doc/html/mammult_docse5.html
new file mode 100644
index 0000000..44ac716
--- /dev/null
+++ b/doc/html/mammult_docse5.html
@@ -0,0 +1,47 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Multiplex networks with inter-layer degree correlations</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 239--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu50.html" >next</a>] [<a
+href="mammult_docsu49.html" >prev</a>] [<a
+href="mammult_docsu49.html#tailmammult_docsu49.html" >prev-tail</a>] [<a
+href="#tailmammult_docse5.html">tail</a>] [<a
+href="mammult_docch2.html#mammult_docse5.html" >up</a>] </p></div>
+ <h3 class="sectionHead"><span class="titlemark">2.3 </span> <a
+ id="x57-560002.3"></a>Multiplex networks with inter-layer degree correlations</h3>
+<!--l. 241--><p class="noindent" >
+ <div class="subsectionTOCS">
+   <span class="subsectionToc" >2.3.1 <a
+href="mammult_docsu50.html#x58-570002.3.1">Models based on simulated annealing</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu51.html#x59-580002.3.1"><span
+class="cmtt-10x-x-109">tune</span><span
+class="cmtt-10x-x-109">_rho</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu52.html#x60-590002.3.1"><span
+class="cmtt-10x-x-109">tune</span><span
+class="cmtt-10x-x-109">_qnn</span><span
+class="cmtt-10x-x-109">_adaptive</span></a></span>
+ </div>
+
+
+
+ <!--l. 247--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu50.html" >next</a>] [<a
+href="mammult_docsu49.html" >prev</a>] [<a
+href="mammult_docsu49.html#tailmammult_docsu49.html" >prev-tail</a>] [<a
+href="mammult_docse5.html" >front</a>] [<a
+href="mammult_docch2.html#mammult_docse5.html" >up</a>] </p></div>
+<!--l. 247--><p class="indent" > <a
+ id="tailmammult_docse5.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docse6.html b/doc/html/mammult_docse6.html
new file mode 100644
index 0000000..fab8160
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@@ -0,0 +1,40 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Interacting opinions - Multilayer ising model</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 249--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu53.html" >next</a>] [<a
+href="mammult_docch3.html" >prev</a>] [<a
+href="mammult_docch3.html#tailmammult_docch3.html" >prev-tail</a>] [<a
+href="#tailmammult_docse6.html">tail</a>] [<a
+href="mammult_docch3.html#mammult_docse6.html" >up</a>] </p></div>
+ <h3 class="sectionHead"><span class="titlemark">3.1 </span> <a
+ id="x62-610003.1"></a>Interacting opinions - Multilayer ising model</h3>
+<!--l. 7--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu53.html#x63-620003.1"><span
+class="cmtt-10x-x-109">multiplex</span><span
+class="cmtt-10x-x-109">_ising</span></a></span>
+ </div>
+
+
+
+ <!--l. 253--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu53.html" >next</a>] [<a
+href="mammult_docch3.html" >prev</a>] [<a
+href="mammult_docch3.html#tailmammult_docch3.html" >prev-tail</a>] [<a
+href="mammult_docse6.html" >front</a>] [<a
+href="mammult_docch3.html#mammult_docse6.html" >up</a>] </p></div>
+<!--l. 253--><p class="indent" > <a
+ id="tailmammult_docse6.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docse7.html b/doc/html/mammult_docse7.html
new file mode 100644
index 0000000..89e367b
--- /dev/null
+++ b/doc/html/mammult_docse7.html
@@ -0,0 +1,49 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Biased random walks</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 253--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu54.html" >next</a>] [<a
+href="mammult_docsu53.html" >prev</a>] [<a
+href="mammult_docsu53.html#tailmammult_docsu53.html" >prev-tail</a>] [<a
+href="#tailmammult_docse7.html">tail</a>] [<a
+href="mammult_docch3.html#mammult_docse7.html" >up</a>] </p></div>
+ <h3 class="sectionHead"><span class="titlemark">3.2 </span> <a
+ id="x64-630003.2"></a>Biased random walks</h3>
+<!--l. 255--><p class="noindent" >
+ <div class="subsectionTOCS">
+   <span class="subsectionToc" >3.2.1 <a
+href="mammult_docsu54.html#x65-640003.2.1">Stationary distribution</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu55.html#x66-650003.2.1"><span
+class="cmtt-10x-x-109">statdistr2</span></a></span>
+<br />   <span class="subsectionToc" >3.2.2 <a
+href="mammult_docsu56.html#x67-660003.2.2">Entropy rate</a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu57.html#x68-670003.2.2"><span
+class="cmtt-10x-x-109">entropyrate2add</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu58.html#x69-680003.2.2"><span
+class="cmtt-10x-x-109">entropyrate2mult</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu59.html#x70-690003.2.2"><span
+class="cmtt-10x-x-109">entropyrate2int</span></a></span>
+ </div>
+<!--l. 265--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu54.html" >next</a>] [<a
+href="mammult_docsu53.html" >prev</a>] [<a
+href="mammult_docsu53.html#tailmammult_docsu53.html" >prev-tail</a>] [<a
+href="mammult_docse7.html" >front</a>] [<a
+href="mammult_docch3.html#mammult_docse7.html" >up</a>] </p></div>
+<!--l. 265--><p class="indent" > <a
+ id="tailmammult_docse7.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu1.html b/doc/html/mammult_docsu1.html
new file mode 100644
index 0000000..6790cf6
--- /dev/null
+++ b/doc/html/mammult_docsu1.html
@@ -0,0 +1,91 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Node and layer activity</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 129--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu2.html" >next</a>] [<a
+href="mammult_docse1.html" >prev</a>] [<a
+href="mammult_docse1.html#tailmammult_docse1.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu1.html">tail</a>] [<a
+href="mammult_docse1.html#mammult_docsu1.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">1.1.1 </span> <a
+ id="x4-30001.1.1"></a>Node and layer activity</h4>
+<!--l. 131--><p class="noindent" >This section includes programs related to the computation of node and layer
+activity, activity vectors, pairwise multiplexity, pairwise normalised Hamming
+distance, node degree vectors.
+<!--l. 7--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu2.html#x5-40001.1.1"><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_activity.py</span></a></span>
+
+
+
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu3.html#x6-50001.1.1"><span
+class="cmtt-10x-x-109">layer</span><span
+class="cmtt-10x-x-109">_activity.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu4.html#x7-60001.1.1"><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_activity</span><span
+class="cmtt-10x-x-109">_vectors.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu5.html#x8-70001.1.1"><span
+class="cmtt-10x-x-109">layer</span><span
+class="cmtt-10x-x-109">_activity</span><span
+class="cmtt-10x-x-109">_vectors.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu6.html#x9-80001.1.1"><span
+class="cmtt-10x-x-109">multiplexity.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu7.html#x10-90001.1.1"><span
+class="cmtt-10x-x-109">hamming</span><span
+class="cmtt-10x-x-109">_dist.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu8.html#x11-100001.1.1"><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_degree</span><span
+class="cmtt-10x-x-109">_vectors.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu9.html#x12-110001.1.1"><span
+class="cmtt-10x-x-109">degs</span><span
+class="cmtt-10x-x-109">_to</span><span
+class="cmtt-10x-x-109">_binary.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu10.html#x13-120001.1.1"><span
+class="cmtt-10x-x-109">degs</span><span
+class="cmtt-10x-x-109">_to</span><span
+class="cmtt-10x-x-109">_activity</span><span
+class="cmtt-10x-x-109">_overlap.py</span></a></span>
+ </div>
+
+
+
+
+
+
+
+
+
+
+
+ <!--l. 145--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu2.html" >next</a>] [<a
+href="mammult_docse1.html" >prev</a>] [<a
+href="mammult_docse1.html#tailmammult_docse1.html" >prev-tail</a>] [<a
+href="mammult_docsu1.html" >front</a>] [<a
+href="mammult_docse1.html#mammult_docsu1.html" >up</a>] </p></div>
+<!--l. 145--><p class="indent" > <a
+ id="tailmammult_docsu1.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu10.html b/doc/html/mammult_docsu10.html
new file mode 100644
index 0000000..99c1c17
--- /dev/null
+++ b/doc/html/mammult_docsu10.html
@@ -0,0 +1,97 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.1.0 degs_to_activity_overlap.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu11.html" >next</a>] [<a
+href="mammult_docsu9.html" >prev</a>] [<a
+href="mammult_docsu9.html#tailmammult_docsu9.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu10.html">tail</a>] [<a
+href="mammult_docsu1.html#mammult_docsu10.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x13-120001.1.1"></a><span
+class="cmtt-10x-x-109">degs</span><span
+class="cmtt-10x-x-109">_to</span><span
+class="cmtt-10x-x-109">_activity</span><span
+class="cmtt-10x-x-109">_overlap.py</span></h5>
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">degs</span><span
+class="cmbx-10x-x-109">_to</span><span
+class="cmbx-10x-x-109">_activity</span><span
+class="cmbx-10x-x-109">_overlap.py </span>- compute the activity and the total
+(overlapping) degree of all the nodes of a multiplex.
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">degs</span><span
+class="cmbx-10x-x-109">_to</span><span
+class="cmbx-10x-x-109">_activity</span><span
+class="cmbx-10x-x-109">_overlap.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">degree</span><span
+class="cmitt-10x-x-109">_vectors</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 14--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 14--><p class="indent" > Take a file which contains, on the n-th line, the degrees at each layer of the
+n-th node, (e.g., the result of the script <span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_degree</span><span
+class="cmtt-10x-x-109">_vectors.py</span>), in the
+format:
+<!--l. 14--><p class="indent" >   <span
+class="cmti-10x-x-109">noden</span><span
+class="cmti-10x-x-109">_deg</span><span
+class="cmti-10x-x-109">_lay1 noden</span><span
+class="cmti-10x-x-109">_deg</span><span
+class="cmti-10x-x-109">_lay2 ... noden</span><span
+class="cmti-10x-x-109">_deg</span><span
+class="cmti-10x-x-109">_layM</span>
+<!--l. 14--><p class="noindent" >and compute the activity (i.e., the number of layers in which a node is not
+isolated) and the total (overlapping) degree of each node.
+<!--l. 26--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 26--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines, where the n-th line contains the
+activity and the total degree of the n-th nodem in the format:
+<!--l. 26--><p class="indent" >   <span
+class="cmti-10x-x-109">noden</span><span
+class="cmti-10x-x-109">_activity noden</span><span
+class="cmti-10x-x-109">_tot</span><span
+class="cmti-10x-x-109">_deg</span>
+<!--l. 26--><p class="noindent" >As usual, the program assumes that node IDs start from zero and proceed
+sequentially, without gaps, i.e., if a node ID is not present in any of the layer
+files given as input, the program considers it as being isolated on all the
+layers.
+<!--l. 28--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 28--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 28--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 145--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu11.html" >next</a>] [<a
+href="mammult_docsu9.html" >prev</a>] [<a
+href="mammult_docsu9.html#tailmammult_docsu9.html" >prev-tail</a>] [<a
+href="mammult_docsu10.html" >front</a>] [<a
+href="mammult_docsu1.html#mammult_docsu10.html" >up</a>] </p></div>
+<!--l. 145--><p class="indent" > <a
+ id="tailmammult_docsu10.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu11.html b/doc/html/mammult_docsu11.html
new file mode 100644
index 0000000..af6ef30
--- /dev/null
+++ b/doc/html/mammult_docsu11.html
@@ -0,0 +1,48 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Layer aggregation</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 145--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu12.html" >next</a>] [<a
+href="mammult_docsu10.html" >prev</a>] [<a
+href="mammult_docsu10.html#tailmammult_docsu10.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu11.html">tail</a>] [<a
+href="mammult_docse1.html#mammult_docsu11.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">1.1.2 </span> <a
+ id="x14-130001.1.2"></a>Layer aggregation</h4>
+<!--l. 147--><p class="noindent" >This section includes programs to obtain various single-layer aggregated graphs
+associated to a multiplex network.
+<!--l. 3--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu12.html#x15-140001.1.2"><span
+class="cmtt-10x-x-109">aggregate</span><span
+class="cmtt-10x-x-109">_layers</span><span
+class="cmtt-10x-x-109">_w.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu13.html#x16-150001.1.2"><span
+class="cmtt-10x-x-109">intersect</span><span
+class="cmtt-10x-x-109">_layers.py</span></a></span>
+ </div>
+
+
+
+
+ <!--l. 153--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu12.html" >next</a>] [<a
+href="mammult_docsu10.html" >prev</a>] [<a
+href="mammult_docsu10.html#tailmammult_docsu10.html" >prev-tail</a>] [<a
+href="mammult_docsu11.html" >front</a>] [<a
+href="mammult_docse1.html#mammult_docsu11.html" >up</a>] </p></div>
+<!--l. 153--><p class="indent" > <a
+ id="tailmammult_docsu11.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu12.html b/doc/html/mammult_docsu12.html
new file mode 100644
index 0000000..2d99541
--- /dev/null
+++ b/doc/html/mammult_docsu12.html
@@ -0,0 +1,104 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.2.0 aggregate_layers_w.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu13.html" >next</a>] [<a
+href="mammult_docsu11.html" >prev</a>] [<a
+href="mammult_docsu11.html#tailmammult_docsu11.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu12.html">tail</a>] [<a
+href="mammult_docsu11.html#mammult_docsu12.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x15-140001.1.2"></a><span
+class="cmtt-10x-x-109">aggregate</span><span
+class="cmtt-10x-x-109">_layers</span><span
+class="cmtt-10x-x-109">_w.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">aggregate</span><span
+class="cmbx-10x-x-109">_layers</span><span
+class="cmbx-10x-x-109">_w.py </span>- compute the (weighted) aggregated graph
+associated to a multiplex.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">aggregate</span><span
+class="cmbx-10x-x-109">_layers</span><span
+class="cmbx-10x-x-109">_w.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer3</span><span
+class="cmmi-10x-x-109">></span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 17--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 17--><p class="indent" > Compute and print on output the edge list of the weighted aggregated graph
+associated to the multiplex network given on input. An edge is present in
+the aggregated graph if it exists in at least one of the M layers of the
+multiplex.
+<!--l. 17--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
+in the format:
+<!--l. 17--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 17--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 28--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 28--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>the edge list of the aggregated graph
+associated to the multiplex network. The edge list is a list of lines in the
+format:
+<!--l. 28--><p class="indent" >   <span
+class="cmti-10x-x-109">ID1 ID2 weight</span>
+
+
+
+<!--l. 28--><p class="noindent" >where <span
+class="cmti-10x-x-109">ID1 </span>and <span
+class="cmti-10x-x-109">ID2 </span>are the IDs of the two nodes and <span
+class="cmti-10x-x-109">weight </span>is the number of
+layers in which an edge between <span
+class="cmti-10x-x-109">ID1 </span>and <span
+class="cmti-10x-x-109">ID2 </span>exists.
+<!--l. 30--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 30--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 30--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu13.html" >next</a>] [<a
+href="mammult_docsu11.html" >prev</a>] [<a
+href="mammult_docsu11.html#tailmammult_docsu11.html" >prev-tail</a>] [<a
+href="mammult_docsu12.html" >front</a>] [<a
+href="mammult_docsu11.html#mammult_docsu12.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu12.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu13.html b/doc/html/mammult_docsu13.html
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--- /dev/null
+++ b/doc/html/mammult_docsu13.html
@@ -0,0 +1,94 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.2.0 intersect_layers.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu14.html" >next</a>] [<a
+href="mammult_docsu12.html" >prev</a>] [<a
+href="mammult_docsu12.html#tailmammult_docsu12.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu13.html">tail</a>] [<a
+href="mammult_docsu11.html#mammult_docsu13.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x16-150001.1.2"></a><span
+class="cmtt-10x-x-109">intersect</span><span
+class="cmtt-10x-x-109">_layers.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">intersect</span><span
+class="cmbx-10x-x-109">_layers.py </span>- compute the intersection graph associated to a
+multiplex.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">intersect</span><span
+class="cmbx-10x-x-109">_layers.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer3</span><span
+class="cmmi-10x-x-109">></span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 16--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 16--><p class="indent" > Compute and print on output the edge list of the intersection graph
+associated to the multiplex network given on input, where an edge exists only if
+it is present on <span
+class="cmbx-10x-x-109">all </span>the layers of the multiplex.
+<!--l. 16--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
+in the format:
+<!--l. 16--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 16--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 26--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 26--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>the edge list of the intersection graph
+associated to the multiplex network. The edge list is a list of lines in the
+format:
+<!--l. 26--><p class="indent" >   <span
+class="cmti-10x-x-109">ID1 ID2</span>
+<!--l. 26--><p class="noindent" >where <span
+class="cmti-10x-x-109">ID1 </span>and <span
+class="cmti-10x-x-109">ID2 </span>are the IDs of the two nodes.
+<!--l. 28--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 28--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 28--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 153--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu14.html" >next</a>] [<a
+href="mammult_docsu12.html" >prev</a>] [<a
+href="mammult_docsu12.html#tailmammult_docsu12.html" >prev-tail</a>] [<a
+href="mammult_docsu13.html" >front</a>] [<a
+href="mammult_docsu11.html#mammult_docsu13.html" >up</a>] </p></div>
+<!--l. 153--><p class="indent" > <a
+ id="tailmammult_docsu13.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu14.html b/doc/html/mammult_docsu14.html
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--- /dev/null
+++ b/doc/html/mammult_docsu14.html
@@ -0,0 +1,61 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Node degree, participation coefficient, cartography</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 153--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu15.html" >next</a>] [<a
+href="mammult_docsu13.html" >prev</a>] [<a
+href="mammult_docsu13.html#tailmammult_docsu13.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu14.html">tail</a>] [<a
+href="mammult_docse1.html#mammult_docsu14.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">1.1.3 </span> <a
+ id="x17-160001.1.3"></a>Node degree, participation coefficient, cartography</h4>
+<!--l. 155--><p class="noindent" >This section includes programs to compute the total degree and participation
+coefficient of each node, and to draw the cartography diagram of a multiplex.
+<!--l. 3--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu15.html#x18-170001.1.3"><span
+class="cmtt-10x-x-109">overlap</span><span
+class="cmtt-10x-x-109">_degree.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu16.html#x19-180001.1.3"><span
+class="cmtt-10x-x-109">cartography</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_layers.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu17.html#x20-190001.1.3"><span
+class="cmtt-10x-x-109">cartography</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_deg</span><span
+class="cmtt-10x-x-109">_vectors.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu18.html#x21-200001.1.3"><span
+class="cmtt-10x-x-109">cartography</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_columns.py</span></a></span>
+ </div>
+
+
+
+
+
+
+ <!--l. 164--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu15.html" >next</a>] [<a
+href="mammult_docsu13.html" >prev</a>] [<a
+href="mammult_docsu13.html#tailmammult_docsu13.html" >prev-tail</a>] [<a
+href="mammult_docsu14.html" >front</a>] [<a
+href="mammult_docse1.html#mammult_docsu14.html" >up</a>] </p></div>
+<!--l. 164--><p class="indent" > <a
+ id="tailmammult_docsu14.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu15.html b/doc/html/mammult_docsu15.html
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--- /dev/null
+++ b/doc/html/mammult_docsu15.html
@@ -0,0 +1,134 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.3.0 overlap_degree.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu16.html" >next</a>] [<a
+href="mammult_docsu14.html" >prev</a>] [<a
+href="mammult_docsu14.html#tailmammult_docsu14.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu15.html">tail</a>] [<a
+href="mammult_docsu14.html#mammult_docsu15.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x18-170001.1.3"></a><span
+class="cmtt-10x-x-109">overlap</span><span
+class="cmtt-10x-x-109">_degree.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">overlap</span><span
+class="cmbx-10x-x-109">_degree.py </span>- compute the total (overlapping) degree of all the nodes
+of a multiplex and the corresponding Z-score.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">overlap</span><span
+class="cmbx-10x-x-109">_degree.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer3</span><span
+class="cmmi-10x-x-109">></span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 29--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 29--><p class="indent" > Compute and print on output the total degree <span
+class="cmmi-10x-x-109">o</span><sub><span
+class="cmmi-8">i</span></sub> of each node <span
+class="cmmi-10x-x-109">i </span>of a
+multiplex, defined as:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc0x.png" alt=" ∑ ∑ [α]
+oi = aij
+ α j
+
+
+
+" class="math-display" ></center></td></tr></table>
+<!--l. 29--><p class="nopar" >
+<!--l. 29--><p class="noindent" >and the corresponding Z-score:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc1x.png" alt=" oi − ⟨o⟩
+z(oi) = ---σ---
+ o
+" class="math-display" ></center></td></tr></table>
+<!--l. 29--><p class="nopar" >
+<!--l. 29--><p class="noindent" >where <span
+class="cmsy-10x-x-109">⟨</span><span
+class="cmmi-10x-x-109">o</span><span
+class="cmsy-10x-x-109">⟩ </span>and <span
+class="cmmi-10x-x-109">σ</span><sub><span
+class="cmmi-8">o</span></sub> are, respectively, the mean and the standard deviation of the
+total degree computed over all the active nodes of the multiplex.
+<!--l. 29--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
+in the format:
+<!--l. 29--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 29--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 43--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 43--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines in the format:
+<!--l. 43--><p class="indent" >   <span
+class="cmti-10x-x-109">ID</span><span
+class="cmti-10x-x-109">_n deg</span><span
+class="cmti-10x-x-109">_n z</span><span
+class="cmti-10x-x-109">_n</span>
+<!--l. 43--><p class="indent" > where <span
+class="cmti-10x-x-109">ID</span><span
+class="cmti-10x-x-109">_n </span>is the ID of the node, <span
+class="cmti-10x-x-109">deg</span><span
+class="cmti-10x-x-109">_n </span>is its total degree, and <span
+class="cmti-10x-x-109">z</span><span
+class="cmti-10x-x-109">_n </span>is the
+corresponding Z-score.
+<!--l. 43--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps, i.e., if
+a node ID is not present in any of the layer files given as input, the program
+considers it as being isolated on all the layers, and the node is omitted from the
+output.
+<!--l. 45--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 45--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">89</span>, 032804 (2014).
+<!--l. 45--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a>
+
+
+
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu16.html" >next</a>] [<a
+href="mammult_docsu14.html" >prev</a>] [<a
+href="mammult_docsu14.html#tailmammult_docsu14.html" >prev-tail</a>] [<a
+href="mammult_docsu15.html" >front</a>] [<a
+href="mammult_docsu14.html#mammult_docsu15.html" >up</a>] </p></div>
+<!--l. 4--><p class="indent" > <a
+ id="tailmammult_docsu15.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu16.html b/doc/html/mammult_docsu16.html
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--- /dev/null
+++ b/doc/html/mammult_docsu16.html
@@ -0,0 +1,144 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.3.0 cartography_from_layers.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu17.html" >next</a>] [<a
+href="mammult_docsu15.html" >prev</a>] [<a
+href="mammult_docsu15.html#tailmammult_docsu15.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu16.html">tail</a>] [<a
+href="mammult_docsu14.html#mammult_docsu16.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x19-180001.1.3"></a><span
+class="cmtt-10x-x-109">cartography</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_layers.py</span></h5>
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">cartography</span><span
+class="cmbx-10x-x-109">_from</span><span
+class="cmbx-10x-x-109">_layers.py </span>- compute the total degree and the multiplex
+participation coefficient of all the nodes of a multiplex.
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">cartography</span><span
+class="cmbx-10x-x-109">_from</span><span
+class="cmbx-10x-x-109">_layers.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer3</span><span
+class="cmmi-10x-x-109">></span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 24--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 24--><p class="indent" > Compute and print on output the total degree and the multiplex
+participation coefficient <span
+class="cmmi-10x-x-109">P</span><sub><span
+class="cmmi-8">i</span></sub> for each node <span
+class="cmmi-10x-x-109">i </span>of a multiplex. The participation
+coefficient is defined as:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc2x.png" alt=" [ M [α] ]
+ -M---- ∑ ki--2
+Pi = M − 1 1 − ( oi )
+ α=1
+" class="math-display" ></center></td></tr></table>
+<!--l. 24--><p class="nopar" >
+<!--l. 24--><p class="noindent" >Note that <span
+class="cmmi-10x-x-109">P</span><sub><span
+class="cmmi-8">i</span></sub> takes values in [0<span
+class="cmmi-10x-x-109">,</span>1], where <span
+class="cmmi-10x-x-109">P</span><sub><span
+class="cmmi-8">i</span></sub> = 0 if and only if node <span
+class="cmmi-10x-x-109">i </span>is active on
+exactly one of the layers, while <span
+class="cmmi-10x-x-109">P</span><sub><span
+class="cmmi-8">i</span></sub> = 1 if node <span
+class="cmmi-10x-x-109">i </span>has equal degree on all the <span
+class="cmmi-10x-x-109">M</span>
+layers.
+<!--l. 24--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
+in the format:
+<!--l. 24--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 24--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 43--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 43--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines in the format:
+
+
+
+<!--l. 43--><p class="indent" >   <span
+class="cmti-10x-x-109">deg</span><span
+class="cmti-10x-x-109">_n P</span><span
+class="cmti-10x-x-109">_n col</span><span
+class="cmti-10x-x-109">_n</span>
+<!--l. 43--><p class="indent" > where <span
+class="cmti-10x-x-109">deg</span><span
+class="cmti-10x-x-109">_n </span>is the total degree of node <span
+class="cmmi-10x-x-109">n</span>, <span
+class="cmti-10x-x-109">P</span><span
+class="cmti-10x-x-109">_n </span>is the participation coefficient
+of node <span
+class="cmmi-10x-x-109">n </span>and <span
+class="cmti-10x-x-109">col </span>is the integer representation of the activity bitstring of node <span
+class="cmmi-10x-x-109">n</span>,
+which is a number between 0 and 2<sup><span
+class="cmmi-8">M</span></sup> <span
+class="cmsy-10x-x-109">− </span>1. The field <span
+class="cmti-10x-x-109">col </span>might be useful for the
+visualisation of the multiplex cartography diagram, where it would be
+possible to associate different colors to nodes having different node activity
+patterns.
+<!--l. 43--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps, i.e.,
+if a node ID is not present in any of the layer files given as input, the
+program considers it as being isolated on all the layers, and is set to
+zero.
+<!--l. 45--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 45--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">89</span>, 032804 (2014).
+<!--l. 45--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu17.html" >next</a>] [<a
+href="mammult_docsu15.html" >prev</a>] [<a
+href="mammult_docsu15.html#tailmammult_docsu15.html" >prev-tail</a>] [<a
+href="mammult_docsu16.html" >front</a>] [<a
+href="mammult_docsu14.html#mammult_docsu16.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu16.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu17.html b/doc/html/mammult_docsu17.html
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--- /dev/null
+++ b/doc/html/mammult_docsu17.html
@@ -0,0 +1,106 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.3.0 cartography_from_deg_vectors.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu18.html" >next</a>] [<a
+href="mammult_docsu16.html" >prev</a>] [<a
+href="mammult_docsu16.html#tailmammult_docsu16.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu17.html">tail</a>] [<a
+href="mammult_docsu14.html#mammult_docsu17.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x20-190001.1.3"></a><span
+class="cmtt-10x-x-109">cartography</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_deg</span><span
+class="cmtt-10x-x-109">_vectors.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">cartography</span><span
+class="cmbx-10x-x-109">_from</span><span
+class="cmbx-10x-x-109">_deg</span><span
+class="cmbx-10x-x-109">_vectors.py </span>- create a multiplex cartography
+diagram.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">cartography</span><span
+class="cmbx-10x-x-109">_from</span><span
+class="cmbx-10x-x-109">_deg</span><span
+class="cmbx-10x-x-109">_vectors.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">node</span><span
+class="cmitt-10x-x-109">_deg</span><span
+class="cmitt-10x-x-109">_vectors</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 14--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 14--><p class="indent" > Compute and print on output the total degree and the multiplex
+participation coefficient of all the nodes of a multiplex network whose
+list of node degree vectors is provided as input. The input file is in the
+format:
+<!--l. 14--><p class="indent" >   <span
+class="cmti-10x-x-109">IDn</span><span
+class="cmti-10x-x-109">_deg1 IDn</span><span
+class="cmti-10x-x-109">_deg</span><span
+class="cmti-10x-x-109">_2 ... IDn</span><span
+class="cmti-10x-x-109">_degM</span>
+<!--l. 14--><p class="noindent" >where <span
+class="cmti-10x-x-109">IDn</span><span
+class="cmti-10x-x-109">_degX </span>is the degree of node <span
+class="cmmi-10x-x-109">n </span>at layer <span
+class="cmmi-10x-x-109">X</span>. The input file can be
+generated using the script <span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_degree</span><span
+class="cmtt-10x-x-109">_vectors.py</span>.
+<!--l. 30--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 30--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines in the format:
+<!--l. 30--><p class="indent" >   <span
+class="cmti-10x-x-109">tot</span><span
+class="cmti-10x-x-109">_deg part</span><span
+class="cmti-10x-x-109">_coeff</span>
+<!--l. 30--><p class="noindent" >where <span
+class="cmti-10x-x-109">tot</span><span
+class="cmti-10x-x-109">_deg </span>is the total degree of the node and <span
+class="cmti-10x-x-109">part</span><span
+class="cmti-10x-x-109">_coeff </span>is the corresponding
+participation coefficient.
+<!--l. 30--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps,
+so if one of the lines in the input files contains just zeros, the program
+considers the corresponding node as being isolated on all the layers, and both
+its total degree and multiplex participation coefficient are set equal to
+zero.
+<!--l. 32--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 32--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">89</span>, 032804 (2014).
+<!--l. 32--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a>
+
+
+
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu18.html" >next</a>] [<a
+href="mammult_docsu16.html" >prev</a>] [<a
+href="mammult_docsu16.html#tailmammult_docsu16.html" >prev-tail</a>] [<a
+href="mammult_docsu17.html" >front</a>] [<a
+href="mammult_docsu14.html#mammult_docsu17.html" >up</a>] </p></div>
+<!--l. 4--><p class="indent" > <a
+ id="tailmammult_docsu17.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu18.html b/doc/html/mammult_docsu18.html
new file mode 100644
index 0000000..ef0ae02
--- /dev/null
+++ b/doc/html/mammult_docsu18.html
@@ -0,0 +1,102 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.3.0 cartography_from_columns.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu19.html" >next</a>] [<a
+href="mammult_docsu17.html" >prev</a>] [<a
+href="mammult_docsu17.html#tailmammult_docsu17.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu18.html">tail</a>] [<a
+href="mammult_docsu14.html#mammult_docsu18.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x21-200001.1.3"></a><span
+class="cmtt-10x-x-109">cartography</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_columns.py</span></h5>
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">cartography</span><span
+class="cmbx-10x-x-109">_from</span><span
+class="cmbx-10x-x-109">_columns.py </span>- compute total and participation
+coefficient of generic structural descriptors of the nodes of a multiplex.
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">cartography</span><span
+class="cmbx-10x-x-109">_from</span><span
+class="cmbx-10x-x-109">_columns.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">filein</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">col1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">col2</span><span
+class="cmmi-10x-x-109">></span>
+<span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">col3</span><span
+class="cmmi-10x-x-109">></span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 22--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 22--><p class="indent" > Compute and print on output the sum and the corresponding participation
+coefficient of a generic structural descriptor of the nodes of a multiplex.
+<!--l. 22--><p class="noindent" >The input file is a generic collection of single-space-separated columns, where
+each line corresponds to a node. The user must specify the IDs of the columns
+which contain the node structural descriptors to be used in the cartography
+diagram. Columns IDs start from ZERO. For example:
+<!--l. 22--><p class="indent" > <span
+class="cmbx-10x-x-109">python cartography</span><span
+class="cmbx-10x-x-109">_from</span><span
+class="cmbx-10x-x-109">_layers.py filein.txt 0 2 4 6 8</span>
+<!--l. 22--><p class="noindent" >will create a cartography diagram assuming that the multiplex network has five
+layers, and that the node structural descriptors at each layers are contained in
+the first (0), third (2), fifth (4), seventh (6) and nineth (8) columns of each
+row.
+<!--l. 33--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 33--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines in the format:
+<!--l. 33--><p class="indent" >   <span
+class="cmti-10x-x-109">tot</span><span
+class="cmti-10x-x-109">_n P</span><span
+class="cmti-10x-x-109">_n</span>
+<!--l. 33--><p class="indent" > where <span
+class="cmti-10x-x-109">tot</span><span
+class="cmti-10x-x-109">_n </span>is the sum over the layers of the considered structural descriptor
+for node <span
+class="cmmi-10x-x-109">n</span>, and <span
+class="cmti-10x-x-109">P</span><span
+class="cmti-10x-x-109">_n </span>is the associated participation coefficient
+<!--l. 35--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 35--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 35--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 164--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu19.html" >next</a>] [<a
+href="mammult_docsu17.html" >prev</a>] [<a
+href="mammult_docsu17.html#tailmammult_docsu17.html" >prev-tail</a>] [<a
+href="mammult_docsu18.html" >front</a>] [<a
+href="mammult_docsu14.html#mammult_docsu18.html" >up</a>] </p></div>
+<!--l. 164--><p class="indent" > <a
+ id="tailmammult_docsu18.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu19.html b/doc/html/mammult_docsu19.html
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--- /dev/null
+++ b/doc/html/mammult_docsu19.html
@@ -0,0 +1,52 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Edge overlap, reinforcement</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 164--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu20.html" >next</a>] [<a
+href="mammult_docsu18.html" >prev</a>] [<a
+href="mammult_docsu18.html#tailmammult_docsu18.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu19.html">tail</a>] [<a
+href="mammult_docse1.html#mammult_docsu19.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">1.1.4 </span> <a
+ id="x22-210001.1.4"></a>Edge overlap, reinforcement</h4>
+<!--l. 165--><p class="noindent" >This section includes programs to compute the egde overlap and to evaulate the
+edge reinforcement effect.
+<!--l. 4--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu20.html#x23-220001.1.4"><span
+class="cmtt-10x-x-109">edge</span><span
+class="cmtt-10x-x-109">_overlap.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu21.html#x24-230001.1.4"><span
+class="cmtt-10x-x-109">avg</span><span
+class="cmtt-10x-x-109">_edge</span><span
+class="cmtt-10x-x-109">_overlap.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu22.html#x25-240001.1.4"><span
+class="cmtt-10x-x-109">reinforcement.py</span></a></span>
+ </div>
+
+
+
+
+
+ <!--l. 172--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu20.html" >next</a>] [<a
+href="mammult_docsu18.html" >prev</a>] [<a
+href="mammult_docsu18.html#tailmammult_docsu18.html" >prev-tail</a>] [<a
+href="mammult_docsu19.html" >front</a>] [<a
+href="mammult_docse1.html#mammult_docsu19.html" >up</a>] </p></div>
+<!--l. 172--><p class="indent" > <a
+ id="tailmammult_docsu19.html"></a>
+</body></html>
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--- /dev/null
+++ b/doc/html/mammult_docsu2.html
@@ -0,0 +1,86 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.1.0 node_activity.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 7--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu3.html" >next</a>] [<a
+href="mammult_docsu1.html" >prev</a>] [<a
+href="mammult_docsu1.html#tailmammult_docsu1.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu2.html">tail</a>] [<a
+href="mammult_docsu1.html#mammult_docsu2.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x5-40001.1.1"></a><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_activity.py</span></h5>
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">node</span><span
+class="cmbx-10x-x-109">_activity.py </span>- compute the activity of the nodes of a multiplex, i.e. the
+number of layers where each node is not isolated.
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">node</span><span
+class="cmbx-10x-x-109">_activity.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 19--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 19--><p class="indent" > Compute and print on output the activity of the nodes of a multiplex
+network, whose layers are given as input in the files <span
+class="cmti-10x-x-109">layer1</span>, <span
+class="cmti-10x-x-109">layer2</span>, etc.
+<!--l. 19--><p class="indent" > Each file contains the (undirected) edge list of a layer, and each line is in the
+format:
+<!--l. 19--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 19--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 22--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 22--><p class="indent" > A list of lines, where the n-th line is the value of activity of the n-th node,
+starting from <span
+class="cmbx-10x-x-109">0</span>.
+<!--l. 24--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 24--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 24--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 8--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu3.html" >next</a>] [<a
+href="mammult_docsu1.html" >prev</a>] [<a
+href="mammult_docsu1.html#tailmammult_docsu1.html" >prev-tail</a>] [<a
+href="mammult_docsu2.html" >front</a>] [<a
+href="mammult_docsu1.html#mammult_docsu2.html" >up</a>] </p></div>
+<!--l. 8--><p class="indent" > <a
+ id="tailmammult_docsu2.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu20.html b/doc/html/mammult_docsu20.html
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--- /dev/null
+++ b/doc/html/mammult_docsu20.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.4.0 edge_overlap.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu21.html" >next</a>] [<a
+href="mammult_docsu19.html" >prev</a>] [<a
+href="mammult_docsu19.html#tailmammult_docsu19.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu20.html">tail</a>] [<a
+href="mammult_docsu19.html#mammult_docsu20.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x23-220001.1.4"></a><span
+class="cmtt-10x-x-109">edge</span><span
+class="cmtt-10x-x-109">_overlap.py</span></h5>
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">edge</span><span
+class="cmbx-10x-x-109">_overlap.py </span>- compute the edge overlap of all the edges of the
+multiplex.
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">edge</span><span
+class="cmbx-10x-x-109">_overlap.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">></span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 25--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 25--><p class="indent" > Compute and print on output the edge overlap <span
+class="cmmi-10x-x-109">o</span><sub><span
+class="cmmi-8">ij</span></sub> of each edge of the
+multiplex. Given a pair of nodes (<span
+class="cmmi-10x-x-109">i,j</span>) that are directly connected on at least one
+of the <span
+class="cmmi-10x-x-109">M </span>layers, the edge overlap <span
+class="cmmi-10x-x-109">o</span><sub><span
+class="cmmi-8">ij</span></sub> is defined as:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc3x.png" alt=" ∑ [α]
+oij = aij
+ α
+
+
+
+" class="math-display" ></center></td></tr></table>
+<!--l. 25--><p class="nopar" >
+<!--l. 25--><p class="noindent" >i.e., the number of layers on which the edge (<span
+class="cmmi-10x-x-109">i,j</span>) exists.
+<!--l. 25--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
+in the format:
+<!--l. 25--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 25--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 34--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 34--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines in the format:
+<!--l. 34--><p class="indent" >   <span
+class="cmti-10x-x-109">ID</span><span
+class="cmti-10x-x-109">_1 ID</span><span
+class="cmti-10x-x-109">_2 overlap</span>
+<!--l. 34--><p class="noindent" >where <span
+class="cmti-10x-x-109">ID</span><span
+class="cmti-10x-x-109">_1 </span>and <span
+class="cmti-10x-x-109">ID</span><span
+class="cmti-10x-x-109">_2 </span>are the IDs of the end-points of the edge, and <span
+class="cmti-10x-x-109">overlap </span>is
+the number of layers in which the edge exists.
+<!--l. 36--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 36--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">89</span>, 032804 (2014).
+<!--l. 36--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu21.html" >next</a>] [<a
+href="mammult_docsu19.html" >prev</a>] [<a
+href="mammult_docsu19.html#tailmammult_docsu19.html" >prev-tail</a>] [<a
+href="mammult_docsu20.html" >front</a>] [<a
+href="mammult_docsu19.html#mammult_docsu20.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu20.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu21.html b/doc/html/mammult_docsu21.html
new file mode 100644
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--- /dev/null
+++ b/doc/html/mammult_docsu21.html
@@ -0,0 +1,125 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.4.0 avg_edge_overlap.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu22.html" >next</a>] [<a
+href="mammult_docsu20.html" >prev</a>] [<a
+href="mammult_docsu20.html#tailmammult_docsu20.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu21.html">tail</a>] [<a
+href="mammult_docsu19.html#mammult_docsu21.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x24-230001.1.4"></a><span
+class="cmtt-10x-x-109">avg</span><span
+class="cmtt-10x-x-109">_edge</span><span
+class="cmtt-10x-x-109">_overlap.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">avg</span><span
+class="cmbx-10x-x-109">_edge</span><span
+class="cmbx-10x-x-109">_overlap.py </span>- compute the average edge overlap of a multiplex.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">avg</span><span
+class="cmbx-10x-x-109">_edge</span><span
+class="cmbx-10x-x-109">_overlap.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">></span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 29--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 29--><p class="indent" > Compute and print on output the average edge overlap
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc4x.png" alt=" ∑ ∑ ∑ [α]
+ ∗ ∑--∑-i--j>i---αaij----
+ω = i j>i(1− δ ∑ [α])
+ 0, α aij
+" class="math-display" ></center></td></tr></table>
+<!--l. 29--><p class="nopar" >
+<!--l. 29--><p class="noindent" >i.e., the expected <span
+class="cmti-10x-x-109">number </span>of layers on which an edge of the multiplex exists, and
+the corresponding normalised quantity:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc5x.png" alt=" ∑ ∑ ∑ a[α]
+ω = ---∑--∑i--j>i--α--ij-----
+ M i j>i(1− δ0,∑α a[iαj] )
+" class="math-display" ></center></td></tr></table>
+<!--l. 29--><p class="nopar" >
+<!--l. 29--><p class="noindent" >that is the expected <span
+class="cmti-10x-x-109">fraction </span>of layers on which an edge of the multiplex is
+present.
+<!--l. 29--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
+in the format:
+<!--l. 29--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 29--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 38--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 38--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a single line, in the format:
+<!--l. 38--><p class="indent" >   <span
+class="cmti-10x-x-109">omega</span><span
+class="cmti-10x-x-109">_star omega</span>
+<!--l. 38--><p class="noindent" >where <span
+class="cmti-10x-x-109">omega</span><span
+class="cmti-10x-x-109">_star </span>and <span
+class="cmti-10x-x-109">omega </span>are, respectively, the expected number and fraction
+of layers in which an edge is present.
+<!--l. 42--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 42--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">89</span>, 032804 (2014).
+<!--l. 42--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a>
+<!--l. 42--><p class="indent" > L. Lacasa, V. Nicosia, V. Latora, <span
+class="cmti-10x-x-109">“Network structure of multivariate time</span>
+<span
+class="cmti-10x-x-109">series”</span>, accepted for publication in Scientific Reports, arxiv:1408.0925
+(2015).
+<!--l. 42--><p class="indent" > Link to paper: <a
+href="http://arxiv.org/abs/1408.0925" class="url" ><span
+class="cmtt-10x-x-109">http://arxiv.org/abs/1408.0925</span></a>
+
+
+
+ <!--l. 7--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu22.html" >next</a>] [<a
+href="mammult_docsu20.html" >prev</a>] [<a
+href="mammult_docsu20.html#tailmammult_docsu20.html" >prev-tail</a>] [<a
+href="mammult_docsu21.html" >front</a>] [<a
+href="mammult_docsu19.html#mammult_docsu21.html" >up</a>] </p></div>
+<!--l. 7--><p class="indent" > <a
+ id="tailmammult_docsu21.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu22.html b/doc/html/mammult_docsu22.html
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@@ -0,0 +1,92 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.4.0 reinforcement.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 7--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse2.html" >next</a>] [<a
+href="mammult_docsu21.html" >prev</a>] [<a
+href="mammult_docsu21.html#tailmammult_docsu21.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu22.html">tail</a>] [<a
+href="mammult_docsu19.html#mammult_docsu22.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x25-240001.1.4"></a><span
+class="cmtt-10x-x-109">reinforcement.py</span></h5>
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">reinforcement.py </span>- compute the probability to have a link between two
+nodes in layer 1 given their weight in layer 2.
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">reinforcement.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> < N</span><sub><span
+class="cmmi-8">bins</span></sub> <span
+class="cmmi-10x-x-109">> < min</span><sub><span
+class="cmmi-8">value</span></sub> <span
+class="cmmi-10x-x-109">></span>
+<span
+class="cmmi-10x-x-109">< max</span><sub><span
+class="cmmi-8">value</span></sub> <span
+class="cmmi-10x-x-109">></span>
+<!--l. 17--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 17--><p class="indent" > Compute and print on output the probability to have a link between two
+nodes in layer 1 given their weight in layer 2. As input are given the files <span
+class="cmti-10x-x-109">layer1</span>,
+<span
+class="cmti-10x-x-109">layer2</span>, the number of bins for the link weights of the second layer, the minimum
+and the maximum values of the binning.
+<!--l. 17--><p class="indent" > The first file contains the binary edge list of layer 1, the second file contains
+the weighted edge list of layer 2. each line is in the format:
+<!--l. 17--><p class="indent" >   <span
+class="cmti-10x-x-109">bin</span><span
+class="cmti-10x-x-109">_min bin</span><span
+class="cmti-10x-x-109">_max freq</span>
+<!--l. 17--><p class="indent" > where <span
+class="cmti-10x-x-109">bin</span><span
+class="cmti-10x-x-109">_min </span>and <span
+class="cmti-10x-x-109">bin</span><span
+class="cmti-10x-x-109">_max </span>are the minimum and maximum values of the
+link weights of layer 2 in that binning, and <span
+class="cmti-10x-x-109">freq </span>is the probability to have a link
+on layer 1 given such weight in layer 2.
+<!--l. 19--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 19--><p class="indent" > A list of lines, where the n-th line is the minimum and maximum values of
+the weight of the links in layer 2 in the n-th bin, and the frequency to have a link
+on layer 2 given that weight.
+<!--l. 21--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 21--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">89</span>, 032804 (2014).
+<!--l. 21--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a>
+
+
+
+ <!--l. 172--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse2.html" >next</a>] [<a
+href="mammult_docsu21.html" >prev</a>] [<a
+href="mammult_docsu21.html#tailmammult_docsu21.html" >prev-tail</a>] [<a
+href="mammult_docsu22.html" >front</a>] [<a
+href="mammult_docsu19.html#mammult_docsu22.html" >up</a>] </p></div>
+<!--l. 172--><p class="indent" > <a
+ id="tailmammult_docsu22.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu23.html b/doc/html/mammult_docsu23.html
new file mode 100644
index 0000000..113a718
--- /dev/null
+++ b/doc/html/mammult_docsu23.html
@@ -0,0 +1,54 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Node ranking</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 174--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu24.html" >next</a>] [<a
+href="mammult_docse2.html" >prev</a>] [<a
+href="mammult_docse2.html#tailmammult_docse2.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu23.html">tail</a>] [<a
+href="mammult_docse2.html#mammult_docsu23.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">1.2.1 </span> <a
+ id="x27-260001.2.1"></a>Node ranking</h4>
+<!--l. 176--><p class="noindent" >This section includes various utilities to compute and compare node rankings
+induced by any generic structural node property, including degree at different
+layers.
+<!--l. 3--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu24.html#x28-270001.2.1"><span
+class="cmtt-10x-x-109">rank</span><span
+class="cmtt-10x-x-109">_nodes.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu25.html#x29-280001.2.1"><span
+class="cmtt-10x-x-109">rank</span><span
+class="cmtt-10x-x-109">_nodes</span><span
+class="cmtt-10x-x-109">_thresh.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu26.html#x30-290001.2.1"><span
+class="cmtt-10x-x-109">rank</span><span
+class="cmtt-10x-x-109">_occurrence.py</span></a></span>
+ </div>
+
+
+
+
+
+ <!--l. 184--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu24.html" >next</a>] [<a
+href="mammult_docse2.html" >prev</a>] [<a
+href="mammult_docse2.html#tailmammult_docse2.html" >prev-tail</a>] [<a
+href="mammult_docsu23.html" >front</a>] [<a
+href="mammult_docse2.html#mammult_docsu23.html" >up</a>] </p></div>
+<!--l. 184--><p class="indent" > <a
+ id="tailmammult_docsu23.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu24.html b/doc/html/mammult_docsu24.html
new file mode 100644
index 0000000..7968150
--- /dev/null
+++ b/doc/html/mammult_docsu24.html
@@ -0,0 +1,79 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.2.1.0 rank_nodes.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu25.html" >next</a>] [<a
+href="mammult_docsu23.html" >prev</a>] [<a
+href="mammult_docsu23.html#tailmammult_docsu23.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu24.html">tail</a>] [<a
+href="mammult_docsu23.html#mammult_docsu24.html" >up</a>] </p></div>
+
+
+
+ <h5 class="subsubsectionHead"><a
+ id="x28-270001.2.1"></a><span
+class="cmtt-10x-x-109">rank</span><span
+class="cmtt-10x-x-109">_nodes.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">rank</span><span
+class="cmbx-10x-x-109">_nodes.py </span>- rank the nodes of a layer according to a given structural
+descriptor.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">rank</span><span
+class="cmbx-10x-x-109">_nodes.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">prop</span><span
+class="cmitt-10x-x-109">_file</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 13--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 13--><p class="indent" > Get a file as input, whose n-th line corresponds to the value of a certain
+property of the n-th node, and rank the nodes according to that property, taking
+into account ranking ties properly.
+<!--l. 13--><p class="indent" > For example, if <span
+class="cmti-10x-x-109">propfile </span>contains the degrees of the nodes at a certain
+layer of the multiplex, the computes the ranking induced by degrees,
+where the node with the highest degree will be assigned a rank equal to <span
+class="cmbx-10x-x-109">1</span>
+(one).
+<!--l. 17--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 17--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines, where the n-th line contains the
+rank of the n-th node corresponding to the values of the structural descriptor
+provided in the input file.
+<!--l. 19--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 19--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 19--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu25.html" >next</a>] [<a
+href="mammult_docsu23.html" >prev</a>] [<a
+href="mammult_docsu23.html#tailmammult_docsu23.html" >prev-tail</a>] [<a
+href="mammult_docsu24.html" >front</a>] [<a
+href="mammult_docsu23.html#mammult_docsu24.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu24.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu25.html b/doc/html/mammult_docsu25.html
new file mode 100644
index 0000000..43094cd
--- /dev/null
+++ b/doc/html/mammult_docsu25.html
@@ -0,0 +1,81 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.2.1.0 rank_nodes_thresh.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu26.html" >next</a>] [<a
+href="mammult_docsu24.html" >prev</a>] [<a
+href="mammult_docsu24.html#tailmammult_docsu24.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu25.html">tail</a>] [<a
+href="mammult_docsu23.html#mammult_docsu25.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x29-280001.2.1"></a><span
+class="cmtt-10x-x-109">rank</span><span
+class="cmtt-10x-x-109">_nodes</span><span
+class="cmtt-10x-x-109">_thresh.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">rank</span><span
+class="cmbx-10x-x-109">_nodes</span><span
+class="cmbx-10x-x-109">_thresh.py </span>- rank the nodes of a layer whose value of a given
+structural descriptor is above a threshold.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">rank</span><span
+class="cmbx-10x-x-109">_nodes</span><span
+class="cmbx-10x-x-109">_thresh.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">prop</span><span
+class="cmitt-10x-x-109">_file</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">thresh</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 10--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 10--><p class="indent" > Get a file as input, whose n-th line corresponds to the value of a certain
+property of the n-th node, and rank the nodes according to that property, taking
+into account ranking ties properly. The rank of all the nodes whose value of the
+structural descriptor is smaller than the threshold <span
+class="cmti-10x-x-109">thresh </span>specified as second
+parameter is set to <span
+class="cmbx-10x-x-109">0 </span>(ZERO).
+<!--l. 16--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 16--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines, where the n-th line contains the
+rank of the n-th node corresponding to the values of the structural descriptor
+provided in the input file, or zero if such desxriptor is below the specified
+threshold <span
+class="cmti-10x-x-109">thresh</span>.
+<!--l. 18--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 18--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 18--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu26.html" >next</a>] [<a
+href="mammult_docsu24.html" >prev</a>] [<a
+href="mammult_docsu24.html#tailmammult_docsu24.html" >prev-tail</a>] [<a
+href="mammult_docsu25.html" >front</a>] [<a
+href="mammult_docsu23.html#mammult_docsu25.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu25.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu26.html b/doc/html/mammult_docsu26.html
new file mode 100644
index 0000000..c13e9a2
--- /dev/null
+++ b/doc/html/mammult_docsu26.html
@@ -0,0 +1,87 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.2.1.0 rank_occurrence.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu27.html" >next</a>] [<a
+href="mammult_docsu25.html" >prev</a>] [<a
+href="mammult_docsu25.html#tailmammult_docsu25.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu26.html">tail</a>] [<a
+href="mammult_docsu23.html#mammult_docsu26.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x30-290001.2.1"></a><span
+class="cmtt-10x-x-109">rank</span><span
+class="cmtt-10x-x-109">_occurrence.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">rank</span><span
+class="cmbx-10x-x-109">_occurrence.py </span>- compute the intersection of two rankings.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">rank</span><span
+class="cmbx-10x-x-109">_occurrence.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">rank1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">rank2</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">increment</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 14--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 14--><p class="indent" > Get two rankings <span
+class="cmti-10x-x-109">rank1 </span>and <span
+class="cmti-10x-x-109">rank2 </span>and compute the size of the <span
+class="cmti-10x-x-109">k</span>-intersection,
+i.e. the number of elements which are present in the first k positions of both
+rankings, as a function of <span
+class="cmti-10x-x-109">k</span>. The parameter <span
+class="cmti-10x-x-109">increment </span>determines the distance
+between two subsequent values of <span
+class="cmti-10x-x-109">k</span>.
+<!--l. 14--><p class="indent" > Each input file is a list of node IDs, one per line, where the first line contains
+the ID of the highest ranked node.
+<!--l. 22--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 22--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines in the format:
+<!--l. 22--><p class="indent" >   <span
+class="cmti-10x-x-109">k num</span><span
+class="cmti-10x-x-109">_k</span>
+<!--l. 22--><p class="indent" > where <span
+class="cmti-10x-x-109">num</span><span
+class="cmti-10x-x-109">_k </span>is the number of nodes which are present in the first <span
+class="cmti-10x-x-109">k </span>positions
+of both rankings.
+<!--l. 24--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 24--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 24--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 184--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu27.html" >next</a>] [<a
+href="mammult_docsu25.html" >prev</a>] [<a
+href="mammult_docsu25.html#tailmammult_docsu25.html" >prev-tail</a>] [<a
+href="mammult_docsu26.html" >front</a>] [<a
+href="mammult_docsu23.html#mammult_docsu26.html" >up</a>] </p></div>
+<!--l. 184--><p class="indent" > <a
+ id="tailmammult_docsu26.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu27.html b/doc/html/mammult_docsu27.html
new file mode 100644
index 0000000..2a20dd4
--- /dev/null
+++ b/doc/html/mammult_docsu27.html
@@ -0,0 +1,52 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Interlayer degree correlation coefficients</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 184--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu28.html" >next</a>] [<a
+href="mammult_docsu26.html" >prev</a>] [<a
+href="mammult_docsu26.html#tailmammult_docsu26.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu27.html">tail</a>] [<a
+href="mammult_docse2.html#mammult_docsu27.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">1.2.2 </span> <a
+ id="x31-300001.2.2"></a>Interlayer degree correlation coefficients</h4>
+<!--l. 186--><p class="noindent" >This section includes programs for the computation of various inter-layer degree
+correlation coefficients.
+<!--l. 4--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu28.html#x32-310001.2.2"><span
+class="cmtt-10x-x-109">compute</span><span
+class="cmtt-10x-x-109">_pearson.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu29.html#x33-320001.2.2"><span
+class="cmtt-10x-x-109">compute</span><span
+class="cmtt-10x-x-109">_rho.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu30.html#x34-330001.2.2"><span
+class="cmtt-10x-x-109">compute</span><span
+class="cmtt-10x-x-109">_tau.py</span></a></span>
+ </div>
+
+
+
+
+
+ <!--l. 194--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu28.html" >next</a>] [<a
+href="mammult_docsu26.html" >prev</a>] [<a
+href="mammult_docsu26.html#tailmammult_docsu26.html" >prev-tail</a>] [<a
+href="mammult_docsu27.html" >front</a>] [<a
+href="mammult_docse2.html#mammult_docsu27.html" >up</a>] </p></div>
+<!--l. 194--><p class="indent" > <a
+ id="tailmammult_docsu27.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu28.html b/doc/html/mammult_docsu28.html
new file mode 100644
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+++ b/doc/html/mammult_docsu28.html
@@ -0,0 +1,96 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.2.2.0 compute_pearson.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
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+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu29.html" >next</a>] [<a
+href="mammult_docsu27.html" >prev</a>] [<a
+href="mammult_docsu27.html#tailmammult_docsu27.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu28.html">tail</a>] [<a
+href="mammult_docsu27.html#mammult_docsu28.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x32-310001.2.2"></a><span
+class="cmtt-10x-x-109">compute</span><span
+class="cmtt-10x-x-109">_pearson.py</span></h5>
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">compute</span><span
+class="cmbx-10x-x-109">_pearson.py </span>- compute the Pearson’s linear correlation coefficient
+between two node properties.
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">compute</span><span
+class="cmbx-10x-x-109">_pearson.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">file1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">file2</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 16--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 16--><p class="indent" > Compute the Pearson’s linear correlation coefficient between two sets of
+(either integer- or real-valued) node properties provided in the input files
+<span
+class="cmti-10x-x-109">file1 </span>and <span
+class="cmti-10x-x-109">file2</span>. Each input file contains a list of lines, where the n-th line
+contains the value of a node property for the n-th node. For instance, <span
+class="cmti-10x-x-109">file1</span>
+and <span
+class="cmti-10x-x-109">file2 </span>might contain the degrees of nodes at two distinct layers of a
+multiplex. However, the program is pretty general and can be used to
+compute the Pearson’s correlation coeffcient between any pairs of node
+properties.
+<!--l. 21--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 21--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>the value of the Pearson’s linear correlation
+coefficient between the two sets of node properties.
+<!--l. 28--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+
+
+
+<!--l. 28--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 28--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+<!--l. 28--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 28--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+<!--l. 28--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and
+condensation in multiplex networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">90</span>, 042807 (2014).
+<!--l. 28--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu29.html" >next</a>] [<a
+href="mammult_docsu27.html" >prev</a>] [<a
+href="mammult_docsu27.html#tailmammult_docsu27.html" >prev-tail</a>] [<a
+href="mammult_docsu28.html" >front</a>] [<a
+href="mammult_docsu27.html#mammult_docsu28.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu28.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu29.html b/doc/html/mammult_docsu29.html
new file mode 100644
index 0000000..973c83d
--- /dev/null
+++ b/doc/html/mammult_docsu29.html
@@ -0,0 +1,100 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.2.2.0 compute_rho.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu30.html" >next</a>] [<a
+href="mammult_docsu28.html" >prev</a>] [<a
+href="mammult_docsu28.html#tailmammult_docsu28.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu29.html">tail</a>] [<a
+href="mammult_docsu27.html#mammult_docsu29.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x33-320001.2.2"></a><span
+class="cmtt-10x-x-109">compute</span><span
+class="cmtt-10x-x-109">_rho.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">compute</span><span
+class="cmbx-10x-x-109">_rho.py </span>- compute the Spearman’s rank correlation coefficient <span
+class="cmmi-10x-x-109">ρ</span>
+between two rankings.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">compute</span><span
+class="cmbx-10x-x-109">_rho.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">file1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">file2</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 20--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 20--><p class="indent" > Compute the Spearman’s rank correlation coefficient <span
+class="cmmi-10x-x-109">ρ </span>between two rankings
+provided in the input files <span
+class="cmti-10x-x-109">file1 </span>and <span
+class="cmti-10x-x-109">file2</span>. Each input file contains a list of lines,
+where the n-th line contains the value of rank of the n-th node. For instance, <span
+class="cmti-10x-x-109">file1</span>
+and <span
+class="cmti-10x-x-109">file2 </span>might contain the ranks of nodes induced by the degree sequences of
+two distinct layers of a multiplex.
+<!--l. 20--><p class="indent" > However, the program is pretty general and can be used to compute
+the Spearman’s rank correlation coefficient between any generic pair of
+rankings.
+<!--l. 20--><p class="indent" > N.B.: A C implementation of this program, with the same interface is also
+available in the executable file <span
+class="cmtt-10x-x-109">compute</span><span
+class="cmtt-10x-x-109">_rho</span>.
+<!--l. 25--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 25--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>the value of the Spearman’s rank correlation
+coefficient <span
+class="cmmi-10x-x-109">ρ </span>between the two rankings provided as input.
+<!--l. 32--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 32--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 32--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+<!--l. 32--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 32--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+<!--l. 32--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and
+condensation in multiplex networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">90</span>, 042807 (2014).
+<!--l. 32--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu30.html" >next</a>] [<a
+href="mammult_docsu28.html" >prev</a>] [<a
+href="mammult_docsu28.html#tailmammult_docsu28.html" >prev-tail</a>] [<a
+href="mammult_docsu29.html" >front</a>] [<a
+href="mammult_docsu27.html#mammult_docsu29.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu29.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu3.html b/doc/html/mammult_docsu3.html
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--- /dev/null
+++ b/doc/html/mammult_docsu3.html
@@ -0,0 +1,87 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.1.0 layer_activity.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 8--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu4.html" >next</a>] [<a
+href="mammult_docsu2.html" >prev</a>] [<a
+href="mammult_docsu2.html#tailmammult_docsu2.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu3.html">tail</a>] [<a
+href="mammult_docsu1.html#mammult_docsu3.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x6-50001.1.1"></a><span
+class="cmtt-10x-x-109">layer</span><span
+class="cmtt-10x-x-109">_activity.py</span></h5>
+<!--l. 8--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 8--><p class="indent" > <span
+class="cmbx-10x-x-109">layer</span><span
+class="cmbx-10x-x-109">_activity.py </span>- compute the activity of the layers of a multiplex, i.e. the
+number of active nodes on each layer.
+<!--l. 8--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 8--><p class="indent" > <span
+class="cmbx-10x-x-109">layer</span><span
+class="cmbx-10x-x-109">_activity.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 20--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 20--><p class="indent" > Compute and print on output the activity of the layers of a multiplex
+network, where the layers are given as input in the files <span
+class="cmti-10x-x-109">layer1</span>, <span
+class="cmti-10x-x-109">layer2</span>,
+etc.
+<!--l. 20--><p class="indent" > Each file contains the (undirected) edge list of a layer, and each line is in the
+format:
+<!--l. 20--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 20--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 23--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 23--><p class="indent" > A listof lines, where the n-th line is the value of activity of the n-th layer,
+starting from <span
+class="cmbx-10x-x-109">0</span>.
+<!--l. 25--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 25--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 25--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu4.html" >next</a>] [<a
+href="mammult_docsu2.html" >prev</a>] [<a
+href="mammult_docsu2.html#tailmammult_docsu2.html" >prev-tail</a>] [<a
+href="mammult_docsu3.html" >front</a>] [<a
+href="mammult_docsu1.html#mammult_docsu3.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu3.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu30.html b/doc/html/mammult_docsu30.html
new file mode 100644
index 0000000..c743f7b
--- /dev/null
+++ b/doc/html/mammult_docsu30.html
@@ -0,0 +1,100 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.2.2.0 compute_tau.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu31.html" >next</a>] [<a
+href="mammult_docsu29.html" >prev</a>] [<a
+href="mammult_docsu29.html#tailmammult_docsu29.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu30.html">tail</a>] [<a
+href="mammult_docsu27.html#mammult_docsu30.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x34-330001.2.2"></a><span
+class="cmtt-10x-x-109">compute</span><span
+class="cmtt-10x-x-109">_tau.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">compute</span><span
+class="cmbx-10x-x-109">_tau.py </span>- compute the Kendall’s rank correlation coefficient <span
+class="cmmi-10x-x-109">τ</span><sub><span
+class="cmmi-8">b</span></sub>
+between two rankings.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">compute</span><span
+class="cmbx-10x-x-109">_tau.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">file1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">file2</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 19--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 19--><p class="indent" > Compute the Kendall’s rank correlation coefficient <span
+class="cmmi-10x-x-109">τ</span><sub><span
+class="cmmi-8">b</span></sub> between two rankings
+provided in the input files <span
+class="cmti-10x-x-109">file1 </span>and <span
+class="cmti-10x-x-109">file2</span>. Each input file contains a list of lines,
+where the n-th line contains the value of rank of the n-th node. For instance, <span
+class="cmti-10x-x-109">file1</span>
+and <span
+class="cmti-10x-x-109">file2 </span>might contain the ranks of nodes induced by the degree sequences of
+two distinct layers of a multiplex.
+<!--l. 19--><p class="indent" > However, the program is pretty general and can be used to compute
+the Kendall’s rank correlation coefficient between any generic pair of
+rankings.
+<!--l. 19--><p class="indent" > N.B.: This implementation takes properly into account rank ties.
+<!--l. 24--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 24--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>the value of the Kendall’s rank correlation
+coefficient <span
+class="cmmi-10x-x-109">τ</span><sub><span
+class="cmmi-8">b</span></sub> between the two rankings provided as input.
+<!--l. 31--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 31--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 31--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+<!--l. 31--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 31--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+<!--l. 31--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and
+condensation in multiplex networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">90</span>, 042807 (2014).
+<!--l. 31--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a>
+
+
+
+ <!--l. 194--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu31.html" >next</a>] [<a
+href="mammult_docsu29.html" >prev</a>] [<a
+href="mammult_docsu29.html#tailmammult_docsu29.html" >prev-tail</a>] [<a
+href="mammult_docsu30.html" >front</a>] [<a
+href="mammult_docsu27.html#mammult_docsu30.html" >up</a>] </p></div>
+<!--l. 194--><p class="indent" > <a
+ id="tailmammult_docsu30.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu31.html b/doc/html/mammult_docsu31.html
new file mode 100644
index 0000000..50ae7f8
--- /dev/null
+++ b/doc/html/mammult_docsu31.html
@@ -0,0 +1,62 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Interlayer degree correlation functions</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 194--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu32.html" >next</a>] [<a
+href="mammult_docsu30.html" >prev</a>] [<a
+href="mammult_docsu30.html#tailmammult_docsu30.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu31.html">tail</a>] [<a
+href="mammult_docse2.html#mammult_docsu31.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">1.2.3 </span> <a
+ id="x35-340001.2.3"></a>Interlayer degree correlation functions</h4>
+<!--l. 196--><p class="noindent" >This section includes programs to compute intra-layer and inter-layer degree
+correlation functions, and to fit those functions with a power-law.
+<!--l. 1--><p class="indent" > M
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu32.html#x36-350001.2.3"><span
+class="cmtt-10x-x-109">dump</span><span
+class="cmtt-10x-x-109">_k</span><span
+class="cmtt-10x-x-109">_q</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu33.html#x37-360001.2.3"><span
+class="cmtt-10x-x-109">knn</span><span
+class="cmtt-10x-x-109">_q</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_layers.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu34.html#x38-370001.2.3"><span
+class="cmtt-10x-x-109">knn</span><span
+class="cmtt-10x-x-109">_q</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_degrees.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu35.html#x39-380001.2.3"><span
+class="cmtt-10x-x-109">fit</span><span
+class="cmtt-10x-x-109">_knn</span></a></span>
+ </div>
+
+
+
+
+
+
+ <!--l. 208--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu32.html" >next</a>] [<a
+href="mammult_docsu30.html" >prev</a>] [<a
+href="mammult_docsu30.html#tailmammult_docsu30.html" >prev-tail</a>] [<a
+href="mammult_docsu31.html" >front</a>] [<a
+href="mammult_docse2.html#mammult_docsu31.html" >up</a>] </p></div>
+<!--l. 208--><p class="indent" > <a
+ id="tailmammult_docsu31.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu32.html b/doc/html/mammult_docsu32.html
new file mode 100644
index 0000000..bfda1c1
--- /dev/null
+++ b/doc/html/mammult_docsu32.html
@@ -0,0 +1,123 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.2.3.0 dump_k_q</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu33.html" >next</a>] [<a
+href="mammult_docsu31.html" >prev</a>] [<a
+href="mammult_docsu31.html#tailmammult_docsu31.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu32.html">tail</a>] [<a
+href="mammult_docsu31.html#mammult_docsu32.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x36-350001.2.3"></a><span
+class="cmtt-10x-x-109">dump</span><span
+class="cmtt-10x-x-109">_k</span><span
+class="cmtt-10x-x-109">_q</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">dump</span><span
+class="cmbx-10x-x-109">_k</span><span
+class="cmbx-10x-x-109">_q </span>- compute the degree sequences of two layers of a multiplex.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">dump</span><span
+class="cmbx-10x-x-109">_k</span><span
+class="cmbx-10x-x-109">_q </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">pairing</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 26--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 26--><p class="indent" > Compute and dump on <span
+class="cmtt-10x-x-109">stdout </span>the degree sequences of two layers of a
+multiplex. The input files <span
+class="cmti-10x-x-109">layer1 </span>and <span
+class="cmti-10x-x-109">layer2 </span>contain the (undirected) edge lists of
+the two layers, and each line is in the format:
+<!--l. 26--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 26--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 26--><p class="indent" > The third file <span
+class="cmti-10x-x-109">pairing </span>is a list of lines in the format:
+<!--l. 26--><p class="indent" >   <span
+class="cmti-10x-x-109">IDL1 IDL2</span>
+<!--l. 26--><p class="indent" > where <span
+class="cmti-10x-x-109">IDL1 </span>is the ID of a node on layer 1 and <span
+class="cmti-10x-x-109">IDL2 </span>is the ID of the same
+node on layer 2. For instance, the line:
+<!--l. 26--><p class="indent" >   <span
+class="cmti-10x-x-109">5 27</span>
+<!--l. 26--><p class="indent" > indicates that node 5 on layer 1 has ID 27 on layer 2.
+<!--l. 35--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+
+
+
+<!--l. 35--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>the degree of each node on the two layers, in
+the format:
+<!--l. 35--><p class="indent" >   <span
+class="cmti-10x-x-109">ki qi</span>
+<!--l. 35--><p class="indent" > where <span
+class="cmti-10x-x-109">ki </span>is the degree of node <span
+class="cmti-10x-x-109">i </span>on layer 1 and <span
+class="cmti-10x-x-109">qi </span>is the degree of node <span
+class="cmti-10x-x-109">i </span>on
+layer 2.
+<!--l. 42--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 42--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 42--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+<!--l. 42--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 42--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+<!--l. 42--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and
+condensation in multiplex networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">90</span>, 042807 (2014).
+<!--l. 42--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu33.html" >next</a>] [<a
+href="mammult_docsu31.html" >prev</a>] [<a
+href="mammult_docsu31.html#tailmammult_docsu31.html" >prev-tail</a>] [<a
+href="mammult_docsu32.html" >front</a>] [<a
+href="mammult_docsu31.html#mammult_docsu32.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu32.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu33.html b/doc/html/mammult_docsu33.html
new file mode 100644
index 0000000..d9b78dd
--- /dev/null
+++ b/doc/html/mammult_docsu33.html
@@ -0,0 +1,233 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.2.3.0 knn_q_from_layers.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu34.html" >next</a>] [<a
+href="mammult_docsu32.html" >prev</a>] [<a
+href="mammult_docsu32.html#tailmammult_docsu32.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu33.html">tail</a>] [<a
+href="mammult_docsu31.html#mammult_docsu33.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x37-360001.2.3"></a><span
+class="cmtt-10x-x-109">knn</span><span
+class="cmtt-10x-x-109">_q</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_layers.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">knn</span><span
+class="cmbx-10x-x-109">_q</span><span
+class="cmbx-10x-x-109">_from</span><span
+class="cmbx-10x-x-109">_layers.py </span>- compute intra-layer and inter-layer degree-degree
+correlation coefficients.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">knn</span><span
+class="cmbx-10x-x-109">_q</span><span
+class="cmbx-10x-x-109">_from</span><span
+class="cmbx-10x-x-109">_layers.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 43--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 43--><p class="indent" > Compute the intra-layer and the inter-layer degree correlation functions for
+two layers given as input. The intra-layer degree correlation function quantifies
+the presence of degree-degree correlations in a single layer network, and is defined
+as:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc6x.png" alt=" --1- ∑ ′ ′
+⟨knn(k)⟩ = kNk k P(k |k )
+ k′
+" class="math-display" ></center></td></tr></table>
+<!--l. 43--><p class="nopar" >
+<!--l. 43--><p class="indent" > where <span
+class="cmmi-10x-x-109">P</span>(<span
+class="cmmi-10x-x-109">k</span><span
+class="cmsy-10x-x-109">′|</span><span
+class="cmmi-10x-x-109">k</span>) is the probability that a neighbour of a node with degree <span
+class="cmmi-10x-x-109">k </span>has
+degree <span
+class="cmmi-10x-x-109">k</span><span
+class="cmsy-10x-x-109">′</span>, and <span
+class="cmmi-10x-x-109">N</span><sub><span
+class="cmmi-8">k</span></sub> is the number of nodes with degree <span
+class="cmmi-10x-x-109">k</span>. The quantity <span
+class="cmsy-10x-x-109">⟨</span><span
+class="cmmi-10x-x-109">k</span><sub><span
+class="cmmi-8">nn</span></sub>(<span
+class="cmmi-10x-x-109">k</span>)<span
+class="cmsy-10x-x-109">⟩ </span>is
+the average degree of the neighbours of nodes having degree equal to
+<span
+class="cmmi-10x-x-109">k</span>.
+<!--l. 43--><p class="indent" > If we consider two layers of a multiplex, and we denote by <span
+class="cmmi-10x-x-109">k </span>the degree
+of a node on the first layer and by <span
+class="cmmi-10x-x-109">q </span>the degree of the same node on
+the second layers, the inter-layer degree correlation function is defined
+as
+ <table
+class="equation-star"><tr><td>
+
+
+
+ <center class="math-display" >
+<img
+src="mammult_doc7x.png" alt="-- ∑ ′ ′
+k(q) = k P(k |q)
+ k′
+" class="math-display" ></center></td></tr></table>
+<!--l. 43--><p class="nopar" >
+<!--l. 43--><p class="indent" > where <span
+class="cmmi-10x-x-109">P</span>(<span
+class="cmmi-10x-x-109">k</span><span
+class="cmsy-10x-x-109">′|</span><span
+class="cmmi-10x-x-109">q</span>) is the probability that a node with degree <span
+class="cmmi-10x-x-109">q </span>on the second layer
+has degree equal to <span
+class="cmmi-10x-x-109">k</span><span
+class="cmsy-10x-x-109">′ </span>on the first layer, and <span
+class="cmmi-10x-x-109">N</span><sub><span
+class="cmmi-8">q</span></sub> is the number of nodes
+with degree <span
+class="cmmi-10x-x-109">q </span>on the second layer. The quantity <span class="overline"><span
+class="cmmi-10x-x-109">k</span></span>(<span
+class="cmmi-10x-x-109">q</span>) is the expected
+degree at layer 1 of node that have degree equal to <span
+class="cmmi-10x-x-109">q </span>on layer 2. The dual
+quantity:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc8x.png" alt="-- ∑ ′ ′
+q(k) = q P(q |k)
+ q′
+" class="math-display" ></center></td></tr></table>
+<!--l. 43--><p class="nopar" >
+<!--l. 43--><p class="indent" > is the average degree on layer 2 of nodes having degree <span
+class="cmmi-10x-x-109">k </span>on layer
+1.
+<!--l. 73--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 73--><p class="indent" > The program creates two output files, respectively called
+<!--l. 73--><p class="indent" >   <span
+class="cmti-10x-x-109">file1</span><span
+class="cmti-10x-x-109">_file2</span><span
+class="cmti-10x-x-109">_k1</span>
+<!--l. 73--><p class="indent" > and
+<!--l. 73--><p class="indent" >   <span
+class="cmti-10x-x-109">file1</span><span
+class="cmti-10x-x-109">_file2</span><span
+class="cmti-10x-x-109">_k2</span>
+<!--l. 73--><p class="indent" > The first file contains a list of lines in the format:
+<!--l. 73--><p class="indent" >   <span
+class="cmti-10x-x-109">k </span><span
+class="cmsy-10x-x-109">⟨</span><span
+class="cmmi-10x-x-109">k</span><sub><span
+class="cmmi-8">nn</span></sub>(<span
+class="cmmi-10x-x-109">k</span>)<span
+class="cmsy-10x-x-109">⟩ </span><span
+class="cmmi-10x-x-109">σ</span><sub><span
+class="cmmi-8">k</span></sub> <span class="overline"><span
+class="cmmi-10x-x-109">q</span></span>(<span
+class="cmmi-10x-x-109">k</span>) <span
+class="cmmi-10x-x-109">σ</span><sub><span class="overline"><span
+class="cmmi-10x-x-109">q</span></span></sub>
+<!--l. 73--><p class="indent" > where <span
+class="cmmi-10x-x-109">k </span>is the degree at first layer, <span
+class="cmsy-10x-x-109">⟨</span><span
+class="cmmi-10x-x-109">k</span><sub><span
+class="cmmi-8">nn</span></sub>(<span
+class="cmmi-10x-x-109">k</span>)<span
+class="cmsy-10x-x-109">⟩ </span>is the average degree of the
+neighbours at layer 1 of nodes having degree <span
+class="cmmi-10x-x-109">k </span>at layer 1, <span
+class="cmmi-10x-x-109">σ</span><sub><span
+class="cmmi-8">k</span></sub> is the standard
+deviation associated to <span
+class="cmsy-10x-x-109">⟨</span><span
+class="cmmi-10x-x-109">k</span><sub><span
+class="cmmi-8">nn</span></sub>(<span
+class="cmmi-10x-x-109">k</span>)<span
+class="cmsy-10x-x-109">⟩</span>, <span class="overline"><span
+class="cmmi-10x-x-109">q</span></span>(<span
+class="cmmi-10x-x-109">k</span>) is the average degree at layer 2 of nodes
+
+
+
+having degree equal to <span
+class="cmmi-10x-x-109">k </span>at layer 1, and <span
+class="cmmi-10x-x-109">σ</span><sub><span class="overline"><span
+class="cmmi-10x-x-109">q</span></span></sub> is the standard deviation associated
+to <span class="overline"><span
+class="cmmi-10x-x-109">q</span></span>(<span
+class="cmmi-10x-x-109">k</span>).
+<!--l. 73--><p class="indent" > The second file contains a similar list of lines, in the format:
+<!--l. 73--><p class="indent" >   <span
+class="cmti-10x-x-109">q </span><span
+class="cmsy-10x-x-109">⟨</span><span
+class="cmmi-10x-x-109">q</span><sub><span
+class="cmmi-8">nn</span></sub>(<span
+class="cmmi-10x-x-109">q</span>)<span
+class="cmsy-10x-x-109">⟩ </span><span
+class="cmmi-10x-x-109">σ</span><sub><span
+class="cmmi-8">q</span></sub> <span class="overline"><span
+class="cmmi-10x-x-109">k</span></span>(<span
+class="cmmi-10x-x-109">q</span>) <span
+class="cmmi-10x-x-109">σ</span><sub><span class="overline"><span
+class="cmmi-10x-x-109">k</span></span></sub>
+<!--l. 73--><p class="indent" > with obvious meaning.
+<!--l. 80--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 80--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 80--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+<!--l. 80--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 80--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+<!--l. 80--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and
+condensation in multiplex networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">90</span>, 042807 (2014).
+<!--l. 80--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu34.html" >next</a>] [<a
+href="mammult_docsu32.html" >prev</a>] [<a
+href="mammult_docsu32.html#tailmammult_docsu32.html" >prev-tail</a>] [<a
+href="mammult_docsu33.html" >front</a>] [<a
+href="mammult_docsu31.html#mammult_docsu33.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu33.html"></a>
+</body></html>
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@@ -0,0 +1,164 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.2.3.0 knn_q_from_degrees.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
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+<!-- html,index=2,3,4,5,next -->
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+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu35.html" >next</a>] [<a
+href="mammult_docsu33.html" >prev</a>] [<a
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+href="#tailmammult_docsu34.html">tail</a>] [<a
+href="mammult_docsu31.html#mammult_docsu34.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x38-370001.2.3"></a><span
+class="cmtt-10x-x-109">knn</span><span
+class="cmtt-10x-x-109">_q</span><span
+class="cmtt-10x-x-109">_from</span><span
+class="cmtt-10x-x-109">_degrees.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">knn</span><span
+class="cmbx-10x-x-109">_q</span><span
+class="cmbx-10x-x-109">_from</span><span
+class="cmbx-10x-x-109">_degrees.py </span>- compute the inter-layer degree-degree
+correlation function.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">knn</span><span
+class="cmbx-10x-x-109">_q</span><span
+class="cmbx-10x-x-109">_from</span><span
+class="cmbx-10x-x-109">_degrees.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">filein</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 37--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 37--><p class="indent" > Compute the inter-layer degree correlation functions for two layers of a
+multiplex, using the degrees of the nodes specified in the input file. The format of
+the input file is as follows
+<!--l. 37--><p class="indent" >   <span
+class="cmti-10x-x-109">ki qi</span>
+<!--l. 37--><p class="indent" > where <span
+class="cmti-10x-x-109">ki </span>and <span
+class="cmti-10x-x-109">qi </span>are, respectively, the degree at layer 1 and the degree at layer
+2 of node <span
+class="cmti-10x-x-109">i</span>.
+<!--l. 37--><p class="indent" > If we consider two layers of a multiplex, and we denote by <span
+class="cmmi-10x-x-109">k </span>the degree
+of a node on the first layer and by <span
+class="cmmi-10x-x-109">q </span>the degree of the same node on
+the second layers, the inter-layer degree correlation function is defined
+as
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc9x.png" alt="k(q) = -1-∑ k′P (k′|q)
+ Nk ′
+ k
+" class="math-display" ></center></td></tr></table>
+<!--l. 37--><p class="nopar" >
+<!--l. 37--><p class="indent" > where <span
+class="cmmi-10x-x-109">P</span>(<span
+class="cmmi-10x-x-109">k</span><span
+class="cmsy-10x-x-109">′|</span><span
+class="cmmi-10x-x-109">q</span>) is the probability that a node with degree <span
+class="cmmi-10x-x-109">q </span>on the second
+layer has degree equal to <span
+class="cmmi-10x-x-109">k</span><span
+class="cmsy-10x-x-109">′ </span>on the first layer, and <span
+class="cmmi-10x-x-109">N</span><sub><span
+class="cmmi-8">k</span></sub> is the number of
+nodes with degree <span
+class="cmmi-10x-x-109">k </span>on the first layer. The quantity <span class="overline"><span
+class="cmmi-10x-x-109">k</span></span>(<span
+class="cmmi-10x-x-109">q</span>) is the expected
+degree at layer 1 of node that have degree equal to <span
+class="cmmi-10x-x-109">q </span>on layer 2. The dual
+
+
+
+quantity:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc10x.png" alt=" ∑
+q(k) = -1- q′P (q′|k)
+ Nq q′
+" class="math-display" ></center></td></tr></table>
+<!--l. 37--><p class="nopar" >
+<!--l. 37--><p class="indent" > is the average degree on layer 2 of nodes having degree <span
+class="cmmi-10x-x-109">k </span>on layer
+1.
+<!--l. 57--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 57--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines in the format:
+<!--l. 57--><p class="indent" >   <span
+class="cmti-10x-x-109">k </span><span class="overline"><span
+class="cmmi-10x-x-109">q</span></span>(<span
+class="cmmi-10x-x-109">k</span>)
+<!--l. 57--><p class="indent" > where <span
+class="cmti-10x-x-109">k </span>is the degree on layer 1 and <span class="overline"><span
+class="cmmi-10x-x-109">q</span></span>(<span
+class="cmmi-10x-x-109">k</span>) is the average degree on layer 2 of
+nodes having degree equal to <span
+class="cmmi-10x-x-109">k </span>on layer 1.
+<!--l. 57--><p class="indent" > The program also prints on <span
+class="cmtt-10x-x-109">stderr </span>a list of lines in the format:
+<!--l. 57--><p class="indent" >   <span
+class="cmti-10x-x-109">q </span><span class="overline"><span
+class="cmmi-10x-x-109">k</span></span>(<span
+class="cmmi-10x-x-109">q</span>)
+<!--l. 57--><p class="indent" > where <span
+class="cmti-10x-x-109">q </span>is the degree on layer 2 and <span class="overline"><span
+class="cmmi-10x-x-109">k</span></span>(<span
+class="cmmi-10x-x-109">q</span>) is the average degree on layer 1 of
+nodes having degree equal to <span
+class="cmmi-10x-x-109">q </span>on layer 2.
+<!--l. 64--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 64--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 64--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+<!--l. 64--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 64--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+<!--l. 64--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and
+condensation in multiplex networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">90</span>, 042807 (2014).
+<!--l. 64--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a>
+
+
+
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu35.html" >next</a>] [<a
+href="mammult_docsu33.html" >prev</a>] [<a
+href="mammult_docsu33.html#tailmammult_docsu33.html" >prev-tail</a>] [<a
+href="mammult_docsu34.html" >front</a>] [<a
+href="mammult_docsu31.html#mammult_docsu34.html" >up</a>] </p></div>
+<!--l. 4--><p class="indent" > <a
+ id="tailmammult_docsu34.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu35.html b/doc/html/mammult_docsu35.html
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--- /dev/null
+++ b/doc/html/mammult_docsu35.html
@@ -0,0 +1,140 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.2.3.0 fit_knn</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docch2.html" >next</a>] [<a
+href="mammult_docsu34.html" >prev</a>] [<a
+href="mammult_docsu34.html#tailmammult_docsu34.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu35.html">tail</a>] [<a
+href="mammult_docsu31.html#mammult_docsu35.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x39-380001.2.3"></a><span
+class="cmtt-10x-x-109">fit</span><span
+class="cmtt-10x-x-109">_knn</span></h5>
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">fit</span><span
+class="cmbx-10x-x-109">_knn </span>- power-law fit of the inter-layer degree correlation function.
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">fit</span><span
+class="cmbx-10x-x-109">_knn </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">filein</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">alpha</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 37--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 37--><p class="indent" > Perform a power-law fit of the inter-layer degree correlation function:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc11x.png" alt="-- 1 ∑
+q(k) = --- q′P (q′|k)
+ Nq q′
+" class="math-display" ></center></td></tr></table>
+<!--l. 37--><p class="nopar" >
+<!--l. 37--><p class="indent" > where <span
+class="cmmi-10x-x-109">k </span>is the degree of a node on layer 1, <span
+class="cmmi-10x-x-109">q </span>is the degree on layer 2 and
+<span
+class="cmmi-10x-x-109">P</span>(<span
+class="cmmi-10x-x-109">q</span><span
+class="cmsy-10x-x-109">|</span><span
+class="cmmi-10x-x-109">k</span>) is the probability that a node with degree <span
+class="cmmi-10x-x-109">k </span>on layer 1 has degree <span
+class="cmmi-10x-x-109">q </span>on
+layer 2. The program assumes that <span class="overline"><span
+class="cmmi-10x-x-109">q</span></span>(<span
+class="cmmi-10x-x-109">k</span>) can be written in the form <span
+class="cmmi-10x-x-109">ak</span><sup><span
+class="cmmi-8">b</span></sup>, and
+computes the two parameters <span
+class="cmmi-10x-x-109">a </span>and <span
+class="cmmi-10x-x-109">b </span>through a linear fit of the log-log plot of
+<span class="overline"><span
+class="cmmi-10x-x-109">q</span></span>(<span
+class="cmmi-10x-x-109">k</span>).
+<!--l. 37--><p class="indent" > The input file <span
+class="cmti-10x-x-109">filein </span>contains a list of lines in the format:
+<!--l. 37--><p class="indent" >   <span
+class="cmti-10x-x-109">ki qi</span>
+<!--l. 37--><p class="indent" > where <span
+class="cmti-10x-x-109">ki </span>is the degree of node <span
+class="cmmi-10x-x-109">i </span>at layer 1 and <span
+class="cmti-10x-x-109">qi </span>is the degree of node <span
+class="cmmi-10x-x-109">i </span>at
+layer 2.
+<!--l. 37--><p class="indent" > The second parameter <span
+class="cmti-10x-x-109">alpha </span>is the ratio of the progression used to generate
+the exponentially-distributed bins for the log-log plot. Typical values of <span
+class="cmti-10x-x-109">alpha </span>are
+between 1<span
+class="cmmi-10x-x-109">.</span>1 and 2<span
+class="cmmi-10x-x-109">.</span>0.
+<!--l. 37--><p class="indent" > N.B.: The exponent <span
+class="cmmi-10x-x-109">b </span>computed with this method is known to be
+inaccurate.
+
+
+
+<!--l. 43--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 43--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>the values of the parameters <span
+class="cmmi-10x-x-109">a </span>and <span
+class="cmmi-10x-x-109">b </span>of the
+power-law fit <span class="overline"><span
+class="cmmi-10x-x-109">q</span></span>(<span
+class="cmmi-10x-x-109">k</span>) = <span
+class="cmmi-10x-x-109">ak</span><sup><span
+class="cmmi-8">b</span></sup>.
+<!--l. 50--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 50--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 50--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+<!--l. 50--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 50--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+<!--l. 50--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and
+condensation in multiplex networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">90</span>, 042807 (2014).
+<!--l. 50--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807</span></a>
+
+
+
+ <!--l. 208--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docch2.html" >next</a>] [<a
+href="mammult_docsu34.html" >prev</a>] [<a
+href="mammult_docsu34.html#tailmammult_docsu34.html" >prev-tail</a>] [<a
+href="mammult_docsu35.html" >front</a>] [<a
+href="mammult_docsu31.html#mammult_docsu35.html" >up</a>] </p></div>
+<!--l. 208--><p class="indent" > <a
+ id="tailmammult_docsu35.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu36.html b/doc/html/mammult_docsu36.html
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@@ -0,0 +1,56 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Null-models of node and layer activity</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
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+<!-- html,index=2,3,4,5,next -->
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+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 212--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu37.html" >next</a>] [<a
+href="mammult_docse3.html" >prev</a>] [<a
+href="mammult_docse3.html#tailmammult_docse3.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu36.html">tail</a>] [<a
+href="mammult_docse3.html#mammult_docsu36.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">2.1.1 </span> <a
+ id="x42-410002.1.1"></a>Null-models of node and layer activity</h4>
+<!--l. 3--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu37.html#x43-420002.1.1"><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_hypergeometric.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu38.html#x44-430002.1.1"><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_MDM.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu39.html#x45-440002.1.1"><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_MSM.py</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu40.html#x46-450002.1.1"><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_layer</span><span
+class="cmtt-10x-x-109">_growth.py</span></a></span>
+ </div>
+
+
+
+
+
+
+ <!--l. 220--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu37.html" >next</a>] [<a
+href="mammult_docse3.html" >prev</a>] [<a
+href="mammult_docse3.html#tailmammult_docse3.html" >prev-tail</a>] [<a
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+href="mammult_docse3.html#mammult_docsu36.html" >up</a>] </p></div>
+<!--l. 220--><p class="indent" > <a
+ id="tailmammult_docsu36.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu37.html b/doc/html/mammult_docsu37.html
new file mode 100644
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--- /dev/null
+++ b/doc/html/mammult_docsu37.html
@@ -0,0 +1,98 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>2.1.1.0 model_hypergeometric.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
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+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu38.html" >next</a>] [<a
+href="mammult_docsu36.html" >prev</a>] [<a
+href="mammult_docsu36.html#tailmammult_docsu36.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu37.html">tail</a>] [<a
+href="mammult_docsu36.html#mammult_docsu37.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x43-420002.1.1"></a><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_hypergeometric.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">model</span><span
+class="cmbx-10x-x-109">_hypergeometric.py </span>- Hypergeometric node activity null
+model.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">model</span><span
+class="cmbx-10x-x-109">_hypergeometric.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer</span><span
+class="cmitt-10x-x-109">_N</span><span
+class="cmitt-10x-x-109">_file</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">N</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 15--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 15--><p class="indent" > This is the hypergeometric model of node activation. In this model each layer
+has exactly the same number of active node of a reference multiplex network, but
+nodes on each layer are activated uniformly at random, thus destroying all
+inter-layer activity correlation patterns.
+<!--l. 15--><p class="indent" > The file <span
+class="cmti-10x-x-109">layer</span><span
+class="cmti-10x-x-109">_N</span><span
+class="cmti-10x-x-109">_file </span>reports on the n-th line the number of active nodes on
+the n-th layer (starting from zero). The second parameter <span
+class="cmti-10x-x-109">N </span>is the total number
+of active nodes in the multiplex.
+<!--l. 31--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 31--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a node-layer list of lines in the format:
+<!--l. 31--><p class="indent" >   <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_i layer</span><span
+class="cmti-10x-x-109">_i</span>
+<!--l. 31--><p class="indent" > where <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_i </span>is the ID of a node and <span
+class="cmti-10x-x-109">layre</span><span
+class="cmti-10x-x-109">_i </span>is the ID of a layer. This
+list indicates which nodes are active in which layer. For instance, the
+line:
+<!--l. 31--><p class="indent" >   <span
+class="cmti-10x-x-109">24 3</span>
+<!--l. 31--><p class="indent" > indicates that the node with ID <span
+class="cmti-10x-x-109">24 </span>is active on layer <span
+class="cmti-10x-x-109">3</span>.
+<!--l. 33--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 33--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 33--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu38.html" >next</a>] [<a
+href="mammult_docsu36.html" >prev</a>] [<a
+href="mammult_docsu36.html#tailmammult_docsu36.html" >prev-tail</a>] [<a
+href="mammult_docsu37.html" >front</a>] [<a
+href="mammult_docsu36.html#mammult_docsu37.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu37.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu38.html b/doc/html/mammult_docsu38.html
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+++ b/doc/html/mammult_docsu38.html
@@ -0,0 +1,106 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>2.1.1.0 model_MDM.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu39.html" >next</a>] [<a
+href="mammult_docsu37.html" >prev</a>] [<a
+href="mammult_docsu37.html#tailmammult_docsu37.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu38.html">tail</a>] [<a
+href="mammult_docsu36.html#mammult_docsu38.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x44-430002.1.1"></a><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_MDM.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">model</span><span
+class="cmbx-10x-x-109">_MDM.py </span>- Multi-activity Deterministic Model.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">model</span><span
+class="cmbx-10x-x-109">_MDM.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">Bi</span><span
+class="cmitt-10x-x-109">_file</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">M</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 23--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 23--><p class="indent" > This is the Multi-activity Deterministic Model (MDM). In this model each
+node <span
+class="cmmi-10x-x-109">i </span>is considered active if it was active in the reference multiplex, maintains
+the same value of node activity <span
+class="cmmi-10x-x-109">B</span><sub><span
+class="cmmi-8">i</span></sub> (i.e., the number of layers in which it was
+active) and is associated an activity vector sampled uniformly at random from
+the <span
+class="cmex-10x-x-109">(</span><span
+class="cmmi-8">M</span>
+ <span
+class="cmmi-8">B</span><sub><span
+class="cmmi-6">i</span></sub><span
+class="cmex-10x-x-109">)</span>
+ possible activity vectors with <span
+class="cmmi-10x-x-109">B</span><sub><span
+class="cmmi-8">i</span></sub> non-null entries.
+<!--l. 23--><p class="indent" > The file <span
+class="cmti-10x-x-109">Bi</span><span
+class="cmti-10x-x-109">_file </span>is in the format:
+<!--l. 23--><p class="indent" >   <span
+class="cmti-10x-x-109">Bi N(Bi)</span>
+<!--l. 23--><p class="indent" > where <span
+class="cmti-10x-x-109">Bi </span>is a value of node activity and <span
+class="cmti-10x-x-109">N(Bi) </span>is the number of nodes which
+had node activity equaly to <span
+class="cmti-10x-x-109">Bi </span>in the reference multiplex.
+<!--l. 23--><p class="indent" > The parameter <span
+class="cmti-10x-x-109">M </span>is the number of layers in the multiplex.
+<!--l. 34--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 34--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a distribution of bit-strings, in the
+format:
+<!--l. 34--><p class="indent" >   <span
+class="cmti-10x-x-109">Bi bitstring count</span>
+<!--l. 34--><p class="indent" > where <span
+class="cmti-10x-x-109">bitstring </span>is the activity bitstring, <span
+class="cmti-10x-x-109">Bi </span>is the number of non-zero entries
+of <span
+class="cmti-10x-x-109">bitstring </span>and <span
+class="cmti-10x-x-109">count </span>is the number of times that <span
+class="cmti-10x-x-109">bitstrings </span>appear in the null
+model.
+<!--l. 37--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 37--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 37--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu39.html" >next</a>] [<a
+href="mammult_docsu37.html" >prev</a>] [<a
+href="mammult_docsu37.html#tailmammult_docsu37.html" >prev-tail</a>] [<a
+href="mammult_docsu38.html" >front</a>] [<a
+href="mammult_docsu36.html#mammult_docsu38.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu38.html"></a>
+</body></html>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>2.1.1.0 model_MSM.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
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+<!-- html,index=2,3,4,5,next -->
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+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu40.html" >next</a>] [<a
+href="mammult_docsu38.html" >prev</a>] [<a
+href="mammult_docsu38.html#tailmammult_docsu38.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu39.html">tail</a>] [<a
+href="mammult_docsu36.html#mammult_docsu39.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x45-440002.1.1"></a><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_MSM.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">model</span><span
+class="cmbx-10x-x-109">_MSM.py </span>- Multi-activity Stochastic Model.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">model</span><span
+class="cmbx-10x-x-109">_MSM.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">node</span><span
+class="cmitt-10x-x-109">_Bi</span><span
+class="cmitt-10x-x-109">_file</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">M</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 21--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 21--><p class="indent" > This is the Multi-activity Stochastic Model (MSM). In this model each node <span
+class="cmmi-10x-x-109">i</span>
+is considered active if it was active in the reference multiplex, and is activated on
+each layer with a probability equal to <span
+class="cmmi-10x-x-109">B</span><sub><span
+class="cmmi-8">i</span></sub><span
+class="cmmi-10x-x-109">∕M </span>where <span
+class="cmmi-10x-x-109">B</span><sub><span
+class="cmmi-8">i</span></sub> was the activity of node <span
+class="cmmi-10x-x-109">i</span>
+in the reference multiplex.
+<!--l. 21--><p class="indent" > The file <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_Bi</span><span
+class="cmti-10x-x-109">_file </span>is in the format:
+<!--l. 21--><p class="indent" >   <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_i Bi)</span>
+<!--l. 21--><p class="indent" > where <span
+class="cmti-10x-x-109">Bi </span>is the value of node activity of <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_i </span>in the reference multiplex.
+<!--l. 21--><p class="indent" > The parameter <span
+class="cmti-10x-x-109">M </span>is the number of layers in the multiplex.
+<!--l. 36--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 36--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a node-layer list of lines in the format:
+<!--l. 36--><p class="indent" >   <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_i layer</span><span
+class="cmti-10x-x-109">_i</span>
+<!--l. 36--><p class="indent" > where <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_i </span>is the ID of a node and <span
+class="cmti-10x-x-109">layre</span><span
+class="cmti-10x-x-109">_i </span>is the ID of a layer. This
+list indicates which nodes are active in which layer. For instance, the
+line:
+<!--l. 36--><p class="indent" >   <span
+class="cmti-10x-x-109">24 3</span>
+<!--l. 36--><p class="indent" > indicates that the node with ID <span
+class="cmti-10x-x-109">24 </span>is active on layer <span
+class="cmti-10x-x-109">3</span>.
+<!--l. 38--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 38--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 38--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu40.html" >next</a>] [<a
+href="mammult_docsu38.html" >prev</a>] [<a
+href="mammult_docsu38.html#tailmammult_docsu38.html" >prev-tail</a>] [<a
+href="mammult_docsu39.html" >front</a>] [<a
+href="mammult_docsu36.html#mammult_docsu39.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu39.html"></a>
+</body></html>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.1.0 node_activity_vectors.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
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+<!-- html,index=2,3,4,5,next -->
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+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu5.html" >next</a>] [<a
+href="mammult_docsu3.html" >prev</a>] [<a
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+href="mammult_docsu1.html#mammult_docsu4.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x7-60001.1.1"></a><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_activity</span><span
+class="cmtt-10x-x-109">_vectors.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">node</span><span
+class="cmbx-10x-x-109">_activity</span><span
+class="cmbx-10x-x-109">_vectors.py </span>- compute the activity vectors of all the nodes of
+a multiplex.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">node</span><span
+class="cmbx-10x-x-109">_activity</span><span
+class="cmbx-10x-x-109">_vectors.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 15--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 15--><p class="indent" > Compute and print on output the activity vectors of the nodes of a
+multiplex network, whose layers are given as input in the files <span
+class="cmti-10x-x-109">layer1</span>, <span
+class="cmti-10x-x-109">layer2</span>,
+etc.
+<!--l. 15--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
+in the format:
+<!--l. 15--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 15--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 26--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 26--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines, where the n-th line contains
+the activity vector of the n-th node, i.e. a bit-string where each bit is
+set to “1” if the node is active on the corresponding layer, and to “0”
+otherwise.
+<!--l. 26--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps, i.e., if
+a node ID is not present in any of the layer files given as input, the program
+considers it as being isolated on all the layers, and will print on output a
+bit-string of zeros.
+<!--l. 28--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 28--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 28--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu5.html" >next</a>] [<a
+href="mammult_docsu3.html" >prev</a>] [<a
+href="mammult_docsu3.html#tailmammult_docsu3.html" >prev-tail</a>] [<a
+href="mammult_docsu4.html" >front</a>] [<a
+href="mammult_docsu1.html#mammult_docsu4.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu4.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu40.html b/doc/html/mammult_docsu40.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>2.1.1.0 model_layer_growth.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
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+<!-- html,index=2,3,4,5,next -->
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+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse4.html" >next</a>] [<a
+href="mammult_docsu39.html" >prev</a>] [<a
+href="mammult_docsu39.html#tailmammult_docsu39.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu40.html">tail</a>] [<a
+href="mammult_docsu36.html#mammult_docsu40.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x46-450002.1.1"></a><span
+class="cmtt-10x-x-109">model</span><span
+class="cmtt-10x-x-109">_layer</span><span
+class="cmtt-10x-x-109">_growth.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">model</span><span
+class="cmbx-10x-x-109">_layer</span><span
+class="cmbx-10x-x-109">_growth.py </span>- Layer growth with preferential activation
+model.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">model</span><span
+class="cmbx-10x-x-109">_layer</span><span
+class="cmbx-10x-x-109">_growth.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer</span><span
+class="cmitt-10x-x-109">_N</span><span
+class="cmitt-10x-x-109">_file</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">N</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">M0</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">A</span><span
+class="cmmi-10x-x-109">></span>
+<span
+class="cmitt-10x-x-109">[RND]</span>
+<!--l. 29--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 29--><p class="indent" > This is the model of layer growth with preferential node activation. In this
+model an entire new layer arrives at time <span
+class="cmmi-10x-x-109">t </span>and a number of nodes <span
+class="cmmi-10x-x-109">N</span><sub><span
+class="cmmi-8">t</span></sub> is
+activated (<span
+class="cmmi-10x-x-109">N</span>_<span
+class="cmmi-10x-x-109">t </span>is equal to the number of nodes active on that layer in the
+reference multiplex). Then, each node <span
+class="cmmi-10x-x-109">i </span>of the new layer is activated with a
+probability:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc12x.png" alt="Pi(t) ∝ A + Bi (t)
+" class="math-display" ></center></td></tr></table>
+<!--l. 29--><p class="nopar" >
+<!--l. 29--><p class="indent" > where <span
+class="cmmi-10x-x-109">B</span><sub><span
+class="cmmi-8">i</span></sub>(<span
+class="cmmi-10x-x-109">t</span>) is the activity of node <span
+class="cmmi-10x-x-109">i </span>at time <span
+class="cmmi-10x-x-109">t </span>(i.e., the number of
+layers in which node <span
+class="cmmi-10x-x-109">i </span>is active at time <span
+class="cmmi-10x-x-109">t</span>) while <span
+class="cmmi-10x-x-109">A > </span>0 is an intrinsic
+attractiveness.
+<!--l. 29--><p class="indent" > The file <span
+class="cmti-10x-x-109">layer</span><span
+class="cmti-10x-x-109">_N</span><span
+class="cmti-10x-x-109">_file </span>reports on the n-th line the number of active nodes on
+the n-th layer.
+<!--l. 29--><p class="indent" > The parameter <span
+class="cmti-10x-x-109">N </span>is the number of nodes in the multiplex, <span
+class="cmti-10x-x-109">M0 </span>is the number
+of layers in the initial network, <span
+class="cmti-10x-x-109">A </span>is the value of node attractiveness.
+<!--l. 29--><p class="indent" > If the user specifies <span
+class="cmtt-10x-x-109">RND </span>as the last parameter, the sequence of layers
+is
+
+
+
+<!--l. 44--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 44--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a node-layer list of lines in the format:
+<!--l. 44--><p class="indent" >   <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_i layer</span><span
+class="cmti-10x-x-109">_i</span>
+<!--l. 44--><p class="indent" > where <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_i </span>is the ID of a node and <span
+class="cmti-10x-x-109">layre</span><span
+class="cmti-10x-x-109">_i </span>is the ID of a layer. This
+list indicates which nodes are active in which layer. For instance, the
+line:
+<!--l. 44--><p class="indent" >   <span
+class="cmti-10x-x-109">24 3</span>
+<!--l. 44--><p class="indent" > indicates that the node with ID <span
+class="cmti-10x-x-109">24 </span>is active on layer <span
+class="cmti-10x-x-109">3</span>.
+<!--l. 46--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 46--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 46--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 220--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse4.html" >next</a>] [<a
+href="mammult_docsu39.html" >prev</a>] [<a
+href="mammult_docsu39.html#tailmammult_docsu39.html" >prev-tail</a>] [<a
+href="mammult_docsu40.html" >front</a>] [<a
+href="mammult_docsu36.html#mammult_docsu40.html" >up</a>] </p></div>
+<!--l. 220--><p class="indent" > <a
+ id="tailmammult_docsu40.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu41.html b/doc/html/mammult_docsu41.html
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+++ b/doc/html/mammult_docsu41.html
@@ -0,0 +1,61 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Linear preferential attachment</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 222--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu42.html" >next</a>] [<a
+href="mammult_docse4.html" >prev</a>] [<a
+href="mammult_docse4.html#tailmammult_docse4.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu41.html">tail</a>] [<a
+href="mammult_docse4.html#mammult_docsu41.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">2.2.1 </span> <a
+ id="x48-470002.2.1"></a>Linear preferential attachment</h4>
+<!--l. 4--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu42.html#x49-480002.2.1"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_delta</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu43.html#x50-490002.2.1"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_delay</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu44.html#x51-500002.2.1"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_delay</span><span
+class="cmtt-10x-x-109">_mix</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu45.html#x52-510002.2.1"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_random</span><span
+class="cmtt-10x-x-109">_times</span></a></span>
+ </div>
+
+
+
+
+
+
+ <!--l. 230--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu42.html" >next</a>] [<a
+href="mammult_docse4.html" >prev</a>] [<a
+href="mammult_docse4.html#tailmammult_docse4.html" >prev-tail</a>] [<a
+href="mammult_docsu41.html" >front</a>] [<a
+href="mammult_docse4.html#mammult_docsu41.html" >up</a>] </p></div>
+<!--l. 230--><p class="indent" > <a
+ id="tailmammult_docsu41.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu42.html b/doc/html/mammult_docsu42.html
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--- /dev/null
+++ b/doc/html/mammult_docsu42.html
@@ -0,0 +1,145 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>2.2.1.0 nibilab_linear_delta</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu43.html" >next</a>] [<a
+href="mammult_docsu41.html" >prev</a>] [<a
+href="mammult_docsu41.html#tailmammult_docsu41.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu42.html">tail</a>] [<a
+href="mammult_docsu41.html#mammult_docsu42.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x49-480002.2.1"></a><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_delta</span></h5>
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">nibilab</span><span
+class="cmbx-10x-x-109">_linear</span><span
+class="cmbx-10x-x-109">_delta </span>- Multiplex linear preferential attachment model –
+Synchronous arrival.
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+
+
+
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">nibilab</span><span
+class="cmbx-10x-x-109">_linear</span><span
+class="cmbx-10x-x-109">_delta </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">N</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">m</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">m0</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">outfile</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">a</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">b</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">c</span><span
+class="cmmi-10x-x-109">></span>
+<span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">d</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 44--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 44--><p class="indent" > Grow a two-layer multiplex network using the multiplex linear preferential
+attachment model by Nicosia, Bianconi, Latora, Barthelemy (NiBiLaB).
+<!--l. 44--><p class="indent" > The probability for a newly arrived node <span
+class="cmmi-10x-x-109">i </span>to create a link to node <span
+class="cmmi-10x-x-109">j </span>on layer
+1 is:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc13x.png" alt="Π1i→j ∝ ak[1j]+ bk[j2]
+" class="math-display" ></center></td></tr></table>
+<!--l. 44--><p class="nopar" >
+<!--l. 44--><p class="indent" > and the dual probability for <span
+class="cmmi-10x-x-109">i </span>to create a link to <span
+class="cmmi-10x-x-109">j </span>on layer 2 is:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc14x.png" alt="Π2 ∝ ck [1]+ dk[2]
+ i→j j j
+" class="math-display" ></center></td></tr></table>
+<!--l. 44--><p class="nopar" >
+<!--l. 44--><p class="indent" > Each new node arrives at the same time on both layers.
+<!--l. 44--><p class="indent" > The (mandatory) parameters are as follows:
+ <ul class="itemize1">
+ <li class="itemize"><span
+class="cmbx-10x-x-109">N </span>number of nodes in the final graph
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">m </span>number of new edges brought by each new node
+
+
+
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">m0 </span>number of nodes in the initial seed graph. <span
+class="cmti-10x-x-109">m0 </span>must be larger than
+ of equal to <span
+class="cmti-10x-x-109">m</span>.
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">outfile </span>the name of the file which will contain the
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">a,b,c,d </span>the coefficients of the attaching probability function
+ </li></ul>
+<!--l. 55--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 55--><p class="indent" > The program dumps on the file <span
+class="cmtt-10x-x-109">outfile </span>the (undirected) edge list of the
+resulting network. Each line of the file is in the format:
+<!--l. 55--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 55--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 57--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 57--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 57--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+
+
+
+ <!--l. 5--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu43.html" >next</a>] [<a
+href="mammult_docsu41.html" >prev</a>] [<a
+href="mammult_docsu41.html#tailmammult_docsu41.html" >prev-tail</a>] [<a
+href="mammult_docsu42.html" >front</a>] [<a
+href="mammult_docsu41.html#mammult_docsu42.html" >up</a>] </p></div>
+<!--l. 5--><p class="indent" > <a
+ id="tailmammult_docsu42.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu43.html b/doc/html/mammult_docsu43.html
new file mode 100644
index 0000000..d88d970
--- /dev/null
+++ b/doc/html/mammult_docsu43.html
@@ -0,0 +1,158 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>2.2.1.0 nibilab_linear_delay</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 5--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu44.html" >next</a>] [<a
+href="mammult_docsu42.html" >prev</a>] [<a
+href="mammult_docsu42.html#tailmammult_docsu42.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu43.html">tail</a>] [<a
+href="mammult_docsu41.html#mammult_docsu43.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x50-490002.2.1"></a><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_delay</span></h5>
+<!--l. 5--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 5--><p class="indent" > <span
+class="cmbx-10x-x-109">nibilab</span><span
+class="cmbx-10x-x-109">_linear</span><span
+class="cmbx-10x-x-109">_delay </span>- Multiplex linear preferential attachment model –
+Asynchronous arrival.
+<!--l. 5--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 5--><p class="indent" > <span
+class="cmbx-10x-x-109">nibilab</span><span
+class="cmbx-10x-x-109">_linear</span><span
+class="cmbx-10x-x-109">_delay </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">N</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">m</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">m0</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">outfile</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">a</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">b</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">c</span><span
+class="cmmi-10x-x-109">></span>
+<span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">d</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">beta</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 54--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 54--><p class="indent" > Grow a two-layer multiplex network using the multiplex linear preferential
+attachment model by Nicosia, Bianconi, Latora, Barthelemy (NiBiLaB).
+<!--l. 54--><p class="indent" > The probability for a newly arrived node <span
+class="cmmi-10x-x-109">i </span>to create a link to node <span
+class="cmmi-10x-x-109">j </span>on layer
+1 is:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc15x.png" alt=" 1 [1] [2]
+Π i→j ∝ akj + bkj
+" class="math-display" ></center></td></tr></table>
+<!--l. 54--><p class="nopar" >
+<!--l. 54--><p class="indent" > and the dual probability for <span
+class="cmmi-10x-x-109">i </span>to create a link to <span
+class="cmmi-10x-x-109">j </span>on layer 2 is:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc16x.png" alt=" 2 [1] [2]
+Π i→j ∝ ck j + dkj
+" class="math-display" ></center></td></tr></table>
+<!--l. 54--><p class="nopar" >
+<!--l. 54--><p class="indent" > Each new node arrives first on layer 1, and its replica on the layer 2 appears
+after a time delay <span
+class="cmmi-10x-x-109">τ </span>sampled from the power-law function:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc17x.png" alt="P(τ) ∼ τ−β
+" class="math-display" ></center></td></tr></table>
+<!--l. 54--><p class="nopar" >
+<!--l. 54--><p class="indent" > The (mandatory) parameters are as follows:
+ <ul class="itemize1">
+ <li class="itemize"><span
+class="cmbx-10x-x-109">N </span>number of nodes in the final graph
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">m </span>number of new edges brought by each new node
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">m0 </span>number of nodes in the initial seed graph. <span
+class="cmti-10x-x-109">m0 </span>must be larger than
+ of equal to <span
+class="cmti-10x-x-109">m</span>.
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">outfile </span>the name of the file which will contain the
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">a,b,c,d </span>the coefficients of the attaching probability function
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">beta </span>the exponent of the power-law delay function which determines
+ the arrival of replicas on layer 2
+ </li></ul>
+
+
+
+<!--l. 65--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 65--><p class="indent" > The program dumps on the file <span
+class="cmtt-10x-x-109">outfile </span>the (undirected) edge list of the
+resulting network. Each line of the file is in the format:
+<!--l. 65--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 65--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 67--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 67--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 67--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+
+
+
+ <!--l. 5--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu44.html" >next</a>] [<a
+href="mammult_docsu42.html" >prev</a>] [<a
+href="mammult_docsu42.html#tailmammult_docsu42.html" >prev-tail</a>] [<a
+href="mammult_docsu43.html" >front</a>] [<a
+href="mammult_docsu41.html#mammult_docsu43.html" >up</a>] </p></div>
+<!--l. 5--><p class="indent" > <a
+ id="tailmammult_docsu43.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu44.html b/doc/html/mammult_docsu44.html
new file mode 100644
index 0000000..2303b84
--- /dev/null
+++ b/doc/html/mammult_docsu44.html
@@ -0,0 +1,163 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>2.2.1.0 nibilab_linear_delay_mix</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 5--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu45.html" >next</a>] [<a
+href="mammult_docsu43.html" >prev</a>] [<a
+href="mammult_docsu43.html#tailmammult_docsu43.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu44.html">tail</a>] [<a
+href="mammult_docsu41.html#mammult_docsu44.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x51-500002.2.1"></a><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_delay</span><span
+class="cmtt-10x-x-109">_mix</span></h5>
+<!--l. 5--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 5--><p class="indent" > <span
+class="cmbx-10x-x-109">nibilab</span><span
+class="cmbx-10x-x-109">_linear</span><span
+class="cmbx-10x-x-109">_delay</span><span
+class="cmbx-10x-x-109">_mix </span>- Multiplex linear preferential attachment model
+– Asynchronous arrival and randomly selected first layer.
+<!--l. 5--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 5--><p class="indent" > <span
+class="cmbx-10x-x-109">nibilab</span><span
+class="cmbx-10x-x-109">_linear</span><span
+class="cmbx-10x-x-109">_delay</span><span
+class="cmbx-10x-x-109">_mix </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">N</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">m</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">m0</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">outfile</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">a</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">b</span><span
+class="cmmi-10x-x-109">></span>
+<span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">c</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">d</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">beta</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 55--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 55--><p class="indent" > Grow a two-layer multiplex network using the multiplex linear preferential
+attachment model by Nicosia, Bianconi, Latora, Barthelemy (NiBiLaB).
+<!--l. 55--><p class="indent" > The probability for a newly arrived node <span
+class="cmmi-10x-x-109">i </span>to create a link to node <span
+class="cmmi-10x-x-109">j </span>on layer
+1 is:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc18x.png" alt=" 1 [1] [2]
+Π i→j ∝ akj + bkj
+" class="math-display" ></center></td></tr></table>
+<!--l. 55--><p class="nopar" >
+<!--l. 55--><p class="indent" > and the dual probability for <span
+class="cmmi-10x-x-109">i </span>to create a link to <span
+class="cmmi-10x-x-109">j </span>on layer 2 is:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc19x.png" alt=" 2 [1] [2]
+Π i→j ∝ ck j + dkj
+" class="math-display" ></center></td></tr></table>
+<!--l. 55--><p class="nopar" >
+<!--l. 55--><p class="indent" > Each new node arrives on one of the two layers, chosen uniformly at random,
+and its replica on the other layer appears after a time delay <span
+class="cmmi-10x-x-109">τ </span>sampled from the
+power-law function:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc20x.png" alt=" −β
+P(τ) ∼ τ
+" class="math-display" ></center></td></tr></table>
+<!--l. 55--><p class="nopar" >
+<!--l. 55--><p class="indent" > The (mandatory) parameters are as follows:
+ <ul class="itemize1">
+ <li class="itemize"><span
+class="cmbx-10x-x-109">N </span>number of nodes in the final graph
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">m </span>number of new edges brought by each new node
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">m0 </span>number of nodes in the initial seed graph. <span
+class="cmti-10x-x-109">m0 </span>must be larger than
+ of equal to <span
+class="cmti-10x-x-109">m</span>.
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">outfile </span>the name of the file which will contain the
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">a,b,c,d </span>the coefficients of the attaching probability function
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">beta </span>the exponent of the power-law delay function which determines
+ the arrival of replicas on layer 2
+ </li></ul>
+
+
+
+<!--l. 66--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 66--><p class="indent" > The program dumps on the file <span
+class="cmtt-10x-x-109">outfile </span>the (undirected) edge list of the
+resulting network. Each line of the file is in the format:
+<!--l. 66--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 66--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 68--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 68--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 68--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+
+
+
+ <!--l. 6--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu45.html" >next</a>] [<a
+href="mammult_docsu43.html" >prev</a>] [<a
+href="mammult_docsu43.html#tailmammult_docsu43.html" >prev-tail</a>] [<a
+href="mammult_docsu44.html" >front</a>] [<a
+href="mammult_docsu41.html#mammult_docsu44.html" >up</a>] </p></div>
+<!--l. 6--><p class="indent" > <a
+ id="tailmammult_docsu44.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu45.html b/doc/html/mammult_docsu45.html
new file mode 100644
index 0000000..28adf3f
--- /dev/null
+++ b/doc/html/mammult_docsu45.html
@@ -0,0 +1,146 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>2.2.1.0 nibilab_linear_random_times</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 6--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu46.html" >next</a>] [<a
+href="mammult_docsu44.html" >prev</a>] [<a
+href="mammult_docsu44.html#tailmammult_docsu44.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu45.html">tail</a>] [<a
+href="mammult_docsu41.html#mammult_docsu45.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x52-510002.2.1"></a><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_linear</span><span
+class="cmtt-10x-x-109">_random</span><span
+class="cmtt-10x-x-109">_times</span></h5>
+<!--l. 6--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 6--><p class="indent" > <span
+class="cmbx-10x-x-109">nibilab</span><span
+class="cmbx-10x-x-109">_linear</span><span
+class="cmbx-10x-x-109">_random</span><span
+class="cmbx-10x-x-109">_times </span>- Multiplex linear preferential attachment
+model – Asynchronous arrival with randomly sampled arrival times on layer
+2.
+<!--l. 6--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 6--><p class="indent" > <span
+class="cmbx-10x-x-109">nibilab</span><span
+class="cmbx-10x-x-109">_linear</span><span
+class="cmbx-10x-x-109">_random</span><span
+class="cmbx-10x-x-109">_times </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">N</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">m</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">m0</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">outfile</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">a</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">b</span><span
+class="cmmi-10x-x-109">></span>
+<span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">c</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">d</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 50--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 50--><p class="indent" > Grow a two-layer multiplex network using the multiplex linear preferential
+attachment model by Nicosia, Bianconi, Latora, Barthelemy (NiBiLaB).
+<!--l. 50--><p class="indent" > The probability for a newly arrived node <span
+class="cmmi-10x-x-109">i </span>to create a link to node <span
+class="cmmi-10x-x-109">j </span>on layer
+1 is:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc21x.png" alt="Π1i→j ∝ ak[1j]+ bk[j2]
+" class="math-display" ></center></td></tr></table>
+<!--l. 50--><p class="nopar" >
+<!--l. 50--><p class="indent" > and the dual probability for <span
+class="cmmi-10x-x-109">i </span>to create a link to <span
+class="cmmi-10x-x-109">j </span>on layer 2 is:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc22x.png" alt=" 2 [1] [2]
+Π i→j ∝ ck j + dkj
+" class="math-display" ></center></td></tr></table>
+<!--l. 50--><p class="nopar" >
+<!--l. 50--><p class="indent" > Each new node arrives on layer 1, but its replica on the other layer appears at
+a uniformly chosen random time in [<span
+class="cmmi-10x-x-109">m</span>0 + 1;<span
+class="cmmi-10x-x-109">N</span>].
+<!--l. 50--><p class="indent" > The (mandatory) parameters are as follows:
+ <ul class="itemize1">
+ <li class="itemize"><span
+class="cmbx-10x-x-109">N </span>number of nodes in the final graph
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">m </span>number of new edges brought by each new node
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">m0 </span>number of nodes in the initial seed graph. <span
+class="cmti-10x-x-109">m0 </span>must be larger than
+ of equal to <span
+class="cmti-10x-x-109">m</span>.
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">outfile </span>the name of the file which will contain the
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">a,b,c,d </span>the coefficients of the attaching probability function
+ </li></ul>
+<!--l. 61--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 61--><p class="indent" > The program dumps on the file <span
+class="cmtt-10x-x-109">outfile </span>the (undirected) edge list of the
+resulting network. Each line of the file is in the format:
+<!--l. 61--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 61--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 63--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 63--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 63--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+
+
+
+ <!--l. 230--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu46.html" >next</a>] [<a
+href="mammult_docsu44.html" >prev</a>] [<a
+href="mammult_docsu44.html#tailmammult_docsu44.html" >prev-tail</a>] [<a
+href="mammult_docsu45.html" >front</a>] [<a
+href="mammult_docsu41.html#mammult_docsu45.html" >up</a>] </p></div>
+<!--l. 230--><p class="indent" > <a
+ id="tailmammult_docsu45.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu46.html b/doc/html/mammult_docsu46.html
new file mode 100644
index 0000000..e3e6edc
--- /dev/null
+++ b/doc/html/mammult_docsu46.html
@@ -0,0 +1,40 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Non-linear preferential attachment</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 230--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu47.html" >next</a>] [<a
+href="mammult_docsu45.html" >prev</a>] [<a
+href="mammult_docsu45.html#tailmammult_docsu45.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu46.html">tail</a>] [<a
+href="mammult_docse4.html#mammult_docsu46.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">2.2.2 </span> <a
+ id="x53-520002.2.2"></a>Non-linear preferential attachment</h4>
+<!--l. 4--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu47.html#x54-530002.2.2"><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_nonlinear</span></a></span>
+ </div>
+
+
+
+ <!--l. 235--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu47.html" >next</a>] [<a
+href="mammult_docsu45.html" >prev</a>] [<a
+href="mammult_docsu45.html#tailmammult_docsu45.html" >prev-tail</a>] [<a
+href="mammult_docsu46.html" >front</a>] [<a
+href="mammult_docse4.html#mammult_docsu46.html" >up</a>] </p></div>
+<!--l. 235--><p class="indent" > <a
+ id="tailmammult_docsu46.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu47.html b/doc/html/mammult_docsu47.html
new file mode 100644
index 0000000..d3d1192
--- /dev/null
+++ b/doc/html/mammult_docsu47.html
@@ -0,0 +1,142 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>2.2.2.0 nibilab_nonlinear</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu48.html" >next</a>] [<a
+href="mammult_docsu46.html" >prev</a>] [<a
+href="mammult_docsu46.html#tailmammult_docsu46.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu47.html">tail</a>] [<a
+href="mammult_docsu46.html#mammult_docsu47.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x54-530002.2.2"></a><span
+class="cmtt-10x-x-109">nibilab</span><span
+class="cmtt-10x-x-109">_nonlinear</span></h5>
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">nibilab</span><span
+class="cmbx-10x-x-109">_nonlinear </span>- Multiplex non-linear preferential attachment model –
+Synchronous arrival.
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">nibilab</span><span
+class="cmbx-10x-x-109">_nonlinear </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">N</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">m</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">m0</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">outfile</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">alpha</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">beta</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 47--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 47--><p class="indent" > Grow a two-layer multiplex network using the multiplex non-linear
+preferential attachment model by Nicosia, Bianconi, Latora, Barthelemy
+(NiBiLaB).
+<!--l. 47--><p class="indent" > The probability for a newly arrived node <span
+class="cmmi-10x-x-109">i </span>to create a link to node <span
+class="cmmi-10x-x-109">j </span>on layer
+1 is:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc23x.png" alt=" ( [1])α
+ 1 kj
+Πi→j ∝ (-[2])β-
+ kj
+" class="math-display" ></center></td></tr></table>
+
+
+
+<!--l. 47--><p class="nopar" >
+<!--l. 47--><p class="indent" > and the dual probability for <span
+class="cmmi-10x-x-109">i </span>to create a link to <span
+class="cmmi-10x-x-109">j </span>on layer 2 is:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc24x.png" alt=" ( )α
+ k[2j]
+Π2i→j ∝ (---)β-
+ k[1j]
+" class="math-display" ></center></td></tr></table>
+<!--l. 47--><p class="nopar" >
+<!--l. 47--><p class="indent" > Each node arrives simultaneously on both layers.
+<!--l. 47--><p class="indent" > The (mandatory) parameters are as follows:
+ <ul class="itemize1">
+ <li class="itemize"><span
+class="cmbx-10x-x-109">N </span>number of nodes in the final graph
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">m </span>number of new edges brought by each new node
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">m0 </span>number of nodes in the initial seed graph. <span
+class="cmti-10x-x-109">m0 </span>must be larger than
+ of equal to <span
+class="cmti-10x-x-109">m</span>.
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">outfile </span>the name of the file which will contain the
+ </li>
+ <li class="itemize"><span
+class="cmbx-10x-x-109">alpha, beta </span>exponents of of the attaching probability function
+ </li></ul>
+<!--l. 58--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 58--><p class="indent" > The program dumps on the file <span
+class="cmtt-10x-x-109">outfile </span>the (undirected) edge list of the
+resulting network. Each line of the file is in the format:
+<!--l. 58--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+
+
+
+<!--l. 58--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 60--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 60--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 60--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+
+
+
+ <!--l. 235--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu48.html" >next</a>] [<a
+href="mammult_docsu46.html" >prev</a>] [<a
+href="mammult_docsu46.html#tailmammult_docsu46.html" >prev-tail</a>] [<a
+href="mammult_docsu47.html" >front</a>] [<a
+href="mammult_docsu46.html#mammult_docsu47.html" >up</a>] </p></div>
+<!--l. 235--><p class="indent" > <a
+ id="tailmammult_docsu47.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu48.html b/doc/html/mammult_docsu48.html
new file mode 100644
index 0000000..d593bbd
--- /dev/null
+++ b/doc/html/mammult_docsu48.html
@@ -0,0 +1,42 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Utilities</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 235--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu49.html" >next</a>] [<a
+href="mammult_docsu47.html" >prev</a>] [<a
+href="mammult_docsu47.html#tailmammult_docsu47.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu48.html">tail</a>] [<a
+href="mammult_docse4.html#mammult_docsu48.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">2.2.3 </span> <a
+ id="x55-540002.2.3"></a>Utilities</h4>
+<!--l. 4--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu49.html#x56-550002.2.3"><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_deg</span><span
+class="cmtt-10x-x-109">_over</span><span
+class="cmtt-10x-x-109">_time.py</span></a></span>
+ </div>
+
+
+
+ <!--l. 239--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu49.html" >next</a>] [<a
+href="mammult_docsu47.html" >prev</a>] [<a
+href="mammult_docsu47.html#tailmammult_docsu47.html" >prev-tail</a>] [<a
+href="mammult_docsu48.html" >front</a>] [<a
+href="mammult_docse4.html#mammult_docsu48.html" >up</a>] </p></div>
+<!--l. 239--><p class="indent" > <a
+ id="tailmammult_docsu48.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu49.html b/doc/html/mammult_docsu49.html
new file mode 100644
index 0000000..fbe3f0c
--- /dev/null
+++ b/doc/html/mammult_docsu49.html
@@ -0,0 +1,145 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>2.2.3.0 node_deg_over_time.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse5.html" >next</a>] [<a
+href="mammult_docsu48.html" >prev</a>] [<a
+href="mammult_docsu48.html#tailmammult_docsu48.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu49.html">tail</a>] [<a
+href="mammult_docsu48.html#mammult_docsu49.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x56-550002.2.3"></a><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_deg</span><span
+class="cmtt-10x-x-109">_over</span><span
+class="cmtt-10x-x-109">_time.py</span></h5>
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">node</span><span
+class="cmbx-10x-x-109">_deg</span><span
+class="cmbx-10x-x-109">_over</span><span
+class="cmbx-10x-x-109">_time.py </span>- Time evolution of the degree of a node in a
+growing graph.
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">node</span><span
+class="cmbx-10x-x-109">_deg</span><span
+class="cmbx-10x-x-109">_over</span><span
+class="cmbx-10x-x-109">_time.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">arrival</span><span
+class="cmitt-10x-x-109">_times</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">node</span><span
+class="cmitt-10x-x-109">_id</span><span
+class="cmmi-10x-x-109">></span>
+<span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">node</span><span
+class="cmitt-10x-x-109">_id</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 30--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 30--><p class="indent" > Compute the degree <span
+class="cmmi-10x-x-109">k</span><sub><span
+class="cmmi-8">i</span></sub>(<span
+class="cmmi-10x-x-109">t</span>) of node <span
+class="cmmi-10x-x-109">i </span>in a growing network as a function of
+time. The file <span
+class="cmti-10x-x-109">layer </span>contains the edge list of the final network. Each line of the
+file is in the format:
+<!--l. 30--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 30--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 30--><p class="indent" > The file <span
+class="cmti-10x-x-109">arrival</span><span
+class="cmti-10x-x-109">_times </span>is a list of node arrival times, in the format:
+<!--l. 30--><p class="indent" >   <span
+class="cmti-10x-x-109">time</span><span
+class="cmti-10x-x-109">_i node</span><span
+class="cmti-10x-x-109">_i</span>
+<!--l. 30--><p class="indent" > where <span
+class="cmti-10x-x-109">time</span><span
+class="cmti-10x-x-109">_i </span>is the time at which <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_i </span>arrived in the graph. Notice that
+<span
+class="cmti-10x-x-109">time</span><span
+class="cmti-10x-x-109">_i </span>must be an integer in the range [0, N-1], where N is the total number of
+nodes in the final graph.
+<!--l. 30--><p class="indent" > The third parameter <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_id </span>is the ID of the node whose degree over time
+will be printed on output. If more than one <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_id </span>is provided, the degrees over
+time of all the corresponding nodes are printed on output.
+<!--l. 48--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 48--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines in the format:
+
+
+
+<!--l. 48--><p class="indent" >   <span
+class="cmti-10x-x-109">t kit</span>
+<!--l. 48--><p class="indent" > where <span
+class="cmti-10x-x-109">kit </span>is the degree of node <span
+class="cmti-10x-x-109">i </span>at time <span
+class="cmti-10x-x-109">t</span>. The first line of output is in the
+format:
+<!--l. 48--><p class="indent" >   <span
+class="cmti-10x-x-109">#### node</span><span
+class="cmti-10x-x-109">_id</span>
+<!--l. 48--><p class="indent" > where <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_id </span>is the ID of node <span
+class="cmti-10x-x-109">i</span>.
+<!--l. 48--><p class="indent" > If more than one <span
+class="cmti-10x-x-109">node</span><span
+class="cmti-10x-x-109">_id</span>s is provided as input, the program prints the degree
+over time of all of them, sequentially.
+<!--l. 50--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 50--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 50--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+
+
+
+ <!--l. 239--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse5.html" >next</a>] [<a
+href="mammult_docsu48.html" >prev</a>] [<a
+href="mammult_docsu48.html#tailmammult_docsu48.html" >prev-tail</a>] [<a
+href="mammult_docsu49.html" >front</a>] [<a
+href="mammult_docsu48.html#mammult_docsu49.html" >up</a>] </p></div>
+<!--l. 239--><p class="indent" > <a
+ id="tailmammult_docsu49.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu5.html b/doc/html/mammult_docsu5.html
new file mode 100644
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--- /dev/null
+++ b/doc/html/mammult_docsu5.html
@@ -0,0 +1,95 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.1.0 layer_activity_vectors.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu6.html" >next</a>] [<a
+href="mammult_docsu4.html" >prev</a>] [<a
+href="mammult_docsu4.html#tailmammult_docsu4.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu5.html">tail</a>] [<a
+href="mammult_docsu1.html#mammult_docsu5.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x8-70001.1.1"></a><span
+class="cmtt-10x-x-109">layer</span><span
+class="cmtt-10x-x-109">_activity</span><span
+class="cmtt-10x-x-109">_vectors.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">layer</span><span
+class="cmbx-10x-x-109">_activity</span><span
+class="cmbx-10x-x-109">_vectors.py </span>- compute the activity vectors of all the layers of
+a multiplex.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">layer</span><span
+class="cmbx-10x-x-109">_activity</span><span
+class="cmbx-10x-x-109">_vectors.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 15--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 15--><p class="indent" > Compute and print on output the activity vectors of the layers of a multiplex
+network, where the layers are given as input in the files <span
+class="cmti-10x-x-109">layer1</span>, <span
+class="cmti-10x-x-109">layer2</span>,
+etc.
+<!--l. 15--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
+in the format:
+<!--l. 15--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 15--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 25--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 25--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines, where the n-th line contains the
+activity vector of the n-th layer, i.e. a bit-string where each bit is set to
+“1” if the corresponding node is active on the n-th layer, and to “0”
+otherwise.
+<!--l. 25--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps, i.e., if
+a node ID is not present in any of the layer files given as input, the program
+considers it as being isolated on all the layers.
+<!--l. 27--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 27--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 27--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu6.html" >next</a>] [<a
+href="mammult_docsu4.html" >prev</a>] [<a
+href="mammult_docsu4.html#tailmammult_docsu4.html" >prev-tail</a>] [<a
+href="mammult_docsu5.html" >front</a>] [<a
+href="mammult_docsu1.html#mammult_docsu5.html" >up</a>] </p></div>
+<!--l. 4--><p class="indent" > <a
+ id="tailmammult_docsu5.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu50.html b/doc/html/mammult_docsu50.html
new file mode 100644
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--- /dev/null
+++ b/doc/html/mammult_docsu50.html
@@ -0,0 +1,46 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Models based on simulated annealing</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 241--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu51.html" >next</a>] [<a
+href="mammult_docse5.html" >prev</a>] [<a
+href="mammult_docse5.html#tailmammult_docse5.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu50.html">tail</a>] [<a
+href="mammult_docse5.html#mammult_docsu50.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">2.3.1 </span> <a
+ id="x58-570002.3.1"></a>Models based on simulated annealing</h4>
+<!--l. 3--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu51.html#x59-580002.3.1"><span
+class="cmtt-10x-x-109">tune</span><span
+class="cmtt-10x-x-109">_rho</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu52.html#x60-590002.3.1"><span
+class="cmtt-10x-x-109">tune</span><span
+class="cmtt-10x-x-109">_qnn</span><span
+class="cmtt-10x-x-109">_adaptive</span></a></span>
+ </div>
+
+
+
+
+ <!--l. 247--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu51.html" >next</a>] [<a
+href="mammult_docse5.html" >prev</a>] [<a
+href="mammult_docse5.html#tailmammult_docse5.html" >prev-tail</a>] [<a
+href="mammult_docsu50.html" >front</a>] [<a
+href="mammult_docse5.html#mammult_docsu50.html" >up</a>] </p></div>
+<!--l. 247--><p class="indent" > <a
+ id="tailmammult_docsu50.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu51.html b/doc/html/mammult_docsu51.html
new file mode 100644
index 0000000..8eab351
--- /dev/null
+++ b/doc/html/mammult_docsu51.html
@@ -0,0 +1,113 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>2.3.1.0 tune_rho</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu52.html" >next</a>] [<a
+href="mammult_docsu50.html" >prev</a>] [<a
+href="mammult_docsu50.html#tailmammult_docsu50.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu51.html">tail</a>] [<a
+href="mammult_docsu50.html#mammult_docsu51.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x59-580002.3.1"></a><span
+class="cmtt-10x-x-109">tune</span><span
+class="cmtt-10x-x-109">_rho</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">tune</span><span
+class="cmbx-10x-x-109">_rho </span>- Construct a multiplex with prescribed inter-layer correlations.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">tune</span><span
+class="cmbx-10x-x-109">_rho </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">rank1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">rank2</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">rho</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">eps</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">beta</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[RND|NAT|INV]</span>
+<!--l. 33--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 33--><p class="indent" > This programs tunes the inter-layer degree correlation coefficient <span
+class="cmmi-10x-x-109">ρ</span>
+(Spearman’s rank correlation) of two layers, by adjusting the inter-layer pairing
+of nodes. The files <span
+class="cmti-10x-x-109">rank1 </span>and <span
+class="cmti-10x-x-109">rank2 </span>are the rankings of nodes in the first and
+second layer, where the n-th line of the file contains the rank of the n-th node
+(the highest ranked node has rank equal to 1).
+
+
+
+<!--l. 33--><p class="indent" > The parameter <span
+class="cmti-10x-x-109">rho </span>is the desired value of the Spearman’s rank correlation
+coefficient, while <span
+class="cmti-10x-x-109">eps </span>is the accuracy of <span
+class="cmti-10x-x-109">rho</span>. For instance, if <span
+class="cmti-10x-x-109">rho </span>is set equal to
+-0.25 and <span
+class="cmti-10x-x-109">eps </span>is equal to 0.0001, the program stops when the configuration of
+node pairing corresponds to a value of <span
+class="cmmi-10x-x-109">ρ </span>which differs from -0.25 by less than
+0.0001.
+<!--l. 33--><p class="indent" > The parameter <span
+class="cmti-10x-x-109">beta </span>is the typical inverse temperature of simulated
+annealing.
+<!--l. 33--><p class="indent" > If no other parameter is specified, or if the last parameter is <span
+class="cmtt-10x-x-109">RND</span>, the program
+starts from a random pairing of nodes. If the last parameter is <span
+class="cmtt-10x-x-109">NAT </span>then the
+program assumes that the initial pairing is the natural one, where the nodes have
+the same ID on both layers. Finally, if <span
+class="cmtt-10x-x-109">INV </span>is specified, the initial pairing is the
+inverse pairing, i.e. the one where node 0 on layer 1 is paired with node N-1 on
+layer 2, and so on.
+<!--l. 43--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 43--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a pairing, i.e. a list of lines in the
+format:
+<!--l. 43--><p class="indent" >   <span
+class="cmti-10x-x-109">IDL1 IDL2</span>
+<!--l. 43--><p class="indent" > where <span
+class="cmti-10x-x-109">IDL1 </span>is the ID of the node on layer 1 and <span
+class="cmti-10x-x-109">IDL2 </span>is the corresponding
+ID of the same node on layer 2.
+<!--l. 45--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 45--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 45--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu52.html" >next</a>] [<a
+href="mammult_docsu50.html" >prev</a>] [<a
+href="mammult_docsu50.html#tailmammult_docsu50.html" >prev-tail</a>] [<a
+href="mammult_docsu51.html" >front</a>] [<a
+href="mammult_docsu50.html#mammult_docsu51.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu51.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu52.html b/doc/html/mammult_docsu52.html
new file mode 100644
index 0000000..b0e0444
--- /dev/null
+++ b/doc/html/mammult_docsu52.html
@@ -0,0 +1,148 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>2.3.1.0 tune_qnn_adaptive</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docch3.html" >next</a>] [<a
+href="mammult_docsu51.html" >prev</a>] [<a
+href="mammult_docsu51.html#tailmammult_docsu51.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu52.html">tail</a>] [<a
+href="mammult_docsu50.html#mammult_docsu52.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x60-590002.3.1"></a><span
+class="cmtt-10x-x-109">tune</span><span
+class="cmtt-10x-x-109">_qnn</span><span
+class="cmtt-10x-x-109">_adaptive</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">tune</span><span
+class="cmbx-10x-x-109">_qnn</span><span
+class="cmbx-10x-x-109">_adaptive </span>- Construct a multiplex with prescribed inter-layer
+correlations.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">tune</span><span
+class="cmbx-10x-x-109">_qnn</span><span
+class="cmbx-10x-x-109">_adaptive </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">degs1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">degs2</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">mu</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">eps</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">beta</span><span
+class="cmmi-10x-x-109">></span>
+<span
+class="cmitt-10x-x-109">[RND|NAT|INV]</span>
+<!--l. 52--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 52--><p class="indent" > This programs tunes the inter-layer degree correlation exponent <span
+class="cmmi-10x-x-109">μ</span>. If
+we consider two layers of a multiplex, and we denote by <span
+class="cmmi-10x-x-109">k </span>the degree
+of a node on the first layer and by <span
+class="cmmi-10x-x-109">q </span>the degree of the same node on
+the second layers, the inter-layer degree correlation function is defined
+as:
+ <table
+class="equation-star"><tr><td>
+ <center class="math-display" >
+<img
+src="mammult_doc25x.png" alt="-- ∑ ′ ′
+q(k) = q P(q |k)
+ q′
+" class="math-display" ></center></td></tr></table>
+<!--l. 52--><p class="nopar" >
+<!--l. 52--><p class="indent" > where <span class="overline"><span
+class="cmmi-10x-x-109">q</span></span>(<span
+class="cmmi-10x-x-109">k</span>) is the average degree on layer 2 of nodes having degree <span
+class="cmmi-10x-x-109">k </span>on layer
+1.
+<!--l. 52--><p class="indent" > The program assumes that we want to set the degree correlation function
+such that:
+ <table
+class="equation-star"><tr><td>
+
+
+
+ <center class="math-display" >
+<img
+src="mammult_doc26x.png" alt="q(k) = akμ
+" class="math-display" ></center></td></tr></table>
+<!--l. 52--><p class="nopar" >
+<!--l. 52--><p class="indent" > where the exponent of the power-law function is given by the user
+(it is indeed the parameter <span
+class="cmti-10x-x-109">mu</span>), and successively adjusts the pairing
+between nodes at the two layers in order to obtain a correlation function as
+close as possible to the desired one. The files <span
+class="cmti-10x-x-109">degs1 </span>and <span
+class="cmti-10x-x-109">degs2 </span>contain,
+respectively, the degrees of the nodes on the first layer and on the second
+layer.
+<!--l. 52--><p class="indent" > The parameter <span
+class="cmti-10x-x-109">eps </span>is the accuracy of <span
+class="cmti-10x-x-109">mu</span>. For instance, if <span
+class="cmti-10x-x-109">mu </span>is set equal to
+-0.25 and <span
+class="cmti-10x-x-109">eps </span>is equal to 0.0001, the program stops when the configuration of
+node pairing corresponds to a value of the exponent <span
+class="cmmi-10x-x-109">μ </span>which differs from -0.25 by
+less than 0.0001.
+<!--l. 52--><p class="indent" > The parameter <span
+class="cmti-10x-x-109">beta </span>is the typical inverse temperature of simulated
+annealing.
+<!--l. 52--><p class="indent" > If no other parameter is specified, or if the last parameter is <span
+class="cmtt-10x-x-109">RND</span>, the program
+starts from a random pairing of nodes. If the last parameter is <span
+class="cmtt-10x-x-109">NAT </span>then the
+program assumes that the initial pairing is the natural one, where the nodes have
+the same ID on both layers. Finally, if <span
+class="cmtt-10x-x-109">INV </span>is specified, the initial pairing is the
+inverse pairing, i.e. the one where node 0 on layer 1 is paired with node N-1 on
+layer 2, and so on.
+<!--l. 62--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 62--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a pairing, i.e. a list of lines in the
+format:
+<!--l. 62--><p class="indent" >   <span
+class="cmti-10x-x-109">IDL1 IDL2</span>
+<!--l. 62--><p class="indent" > where <span
+class="cmti-10x-x-109">IDL1 </span>is the ID of the node on layer 1 and <span
+class="cmti-10x-x-109">IDL2 </span>is the corresponding
+ID of the same node on layer 2.
+<!--l. 64--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 64--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 64--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 247--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docch3.html" >next</a>] [<a
+href="mammult_docsu51.html" >prev</a>] [<a
+href="mammult_docsu51.html#tailmammult_docsu51.html" >prev-tail</a>] [<a
+href="mammult_docsu52.html" >front</a>] [<a
+href="mammult_docsu50.html#mammult_docsu52.html" >up</a>] </p></div>
+<!--l. 247--><p class="indent" > <a
+ id="tailmammult_docsu52.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu53.html b/doc/html/mammult_docsu53.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>3.1.0.0 multiplex_ising</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 7--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse7.html" >next</a>] [<a
+href="mammult_docse6.html" >prev</a>] [<a
+href="mammult_docse6.html#tailmammult_docse6.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu53.html">tail</a>] [<a
+href="mammult_docse6.html#mammult_docsu53.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x63-620003.1"></a><span
+class="cmtt-10x-x-109">multiplex</span><span
+class="cmtt-10x-x-109">_ising</span></h5>
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">multiplex</span><span
+class="cmbx-10x-x-109">_ising </span>- compute the coupled ising model in a multiplex with 2
+layers.
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">multiplex</span><span
+class="cmbx-10x-x-109">_ising </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">T</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">J</span><span
+class="cmmi-10x-x-109">> < γ > < h</span><sup><span
+class="cmr-8">[1]</span></sup> <span
+class="cmmi-10x-x-109">></span>
+<span
+class="cmmi-10x-x-109">< h</span><sup><span
+class="cmr-8">[2]</span></sup> <span
+class="cmmi-10x-x-109">> < p</span><sub><span
+class="cmr-8">1</span></sub> <span
+class="cmmi-10x-x-109">> < p</span><sub><span
+class="cmr-8">2</span></sub> <span
+class="cmmi-10x-x-109">> < numepochs ></span>
+<!--l. 18--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 18--><p class="indent" > Compute and print the output of the ising dynamics on two coupled layers of
+a multiplex network. Files <span
+class="cmti-10x-x-109">layer1</span>, <span
+class="cmti-10x-x-109">layer2</span>, contain the (undirected) edge list of the
+two layer, and each line is in the format:
+<!--l. 18--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 18--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 18--><p class="indent" > <span
+class="cmmi-10x-x-109">T </span>is the value of thermal noise in the system, <span
+class="cmmi-10x-x-109">J </span>the value of peer pressure, <span
+class="cmmi-10x-x-109">γ</span>
+the relative ratio between internal coupling and peer pressure, <span
+class="cmmi-10x-x-109">h</span><sup><span
+class="cmr-8">[1]</span></sup> and <span
+class="cmmi-10x-x-109">h</span><sup><span
+class="cmr-8">[2]</span></sup> the
+external fields acting on the two layers, <span
+class="cmmi-10x-x-109">p</span><sub><span
+class="cmr-8">1</span></sub> the probability for a spin on layer 1 at
+<span
+class="cmmi-10x-x-109">t </span>= 0 to be up, <span
+class="cmmi-10x-x-109">p</span><sub><span
+class="cmr-8">2</span></sub> the same probability for spins on layer 2, <span
+class="cmmi-10x-x-109">numepochs </span>the
+
+
+
+number of epochs for the simulation.
+<!--l. 20--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 20--><p class="indent" > One line, reporting all controlling parameter, the value of consensus in
+layer 1 <span
+class="cmmi-10x-x-109">m</span><sup><span
+class="cmr-8">[1]</span></sup>, the value of consensus in layer 2 <span
+class="cmmi-10x-x-109">m</span><sup><span
+class="cmr-8">[2]</span></sup> and the coherence
+<span
+class="cmmi-10x-x-109">C</span>.
+<!--l. 22--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 22--><p class="indent" > F. Battiston, A. Cairoli, V. Nicosia, A. Baule, V. Latora, <span
+class="cmti-10x-x-109">“Interplay between</span>
+<span
+class="cmti-10x-x-109">consensus and coherence in a model of interacting opinions”</span>, accepted for
+publication in Physica D, arxiv:1506.04544 (2015).
+<!--l. 22--><p class="indent" > Link to paper: <a
+href="http://arxiv.org/abs/1506.04544" class="url" ><span
+class="cmtt-10x-x-109">http://arxiv.org/abs/1506.04544</span></a>
+
+
+
+ <!--l. 253--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docse7.html" >next</a>] [<a
+href="mammult_docse6.html" >prev</a>] [<a
+href="mammult_docse6.html#tailmammult_docse6.html" >prev-tail</a>] [<a
+href="mammult_docsu53.html" >front</a>] [<a
+href="mammult_docse6.html#mammult_docsu53.html" >up</a>] </p></div>
+<!--l. 253--><p class="indent" > <a
+ id="tailmammult_docsu53.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu54.html b/doc/html/mammult_docsu54.html
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--- /dev/null
+++ b/doc/html/mammult_docsu54.html
@@ -0,0 +1,39 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Stationary distribution</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 255--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu55.html" >next</a>] [<a
+href="mammult_docse7.html" >prev</a>] [<a
+href="mammult_docse7.html#tailmammult_docse7.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu54.html">tail</a>] [<a
+href="mammult_docse7.html#mammult_docsu54.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">3.2.1 </span> <a
+ id="x65-640003.2.1"></a>Stationary distribution</h4>
+<!--l. 7--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu55.html#x66-650003.2.1"><span
+class="cmtt-10x-x-109">statdistr2</span></a></span>
+ </div>
+
+
+
+ <!--l. 259--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu55.html" >next</a>] [<a
+href="mammult_docse7.html" >prev</a>] [<a
+href="mammult_docse7.html#tailmammult_docse7.html" >prev-tail</a>] [<a
+href="mammult_docsu54.html" >front</a>] [<a
+href="mammult_docse7.html#mammult_docsu54.html" >up</a>] </p></div>
+<!--l. 259--><p class="indent" > <a
+ id="tailmammult_docsu54.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu55.html b/doc/html/mammult_docsu55.html
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+++ b/doc/html/mammult_docsu55.html
@@ -0,0 +1,121 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>3.2.1.0 statdistr2</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 7--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu56.html" >next</a>] [<a
+href="mammult_docsu54.html" >prev</a>] [<a
+href="mammult_docsu54.html#tailmammult_docsu54.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu55.html">tail</a>] [<a
+href="mammult_docsu54.html#mammult_docsu55.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x66-650003.2.1"></a><span
+class="cmtt-10x-x-109">statdistr2</span></h5>
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">statdistr2 </span>- compute the stationary distribution of additive, multiplicative
+and intensive biased walks in a multiplex with 2 layers.
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">statdistr2 </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> < overlappingnetwork > <</span><span
+class="cmitt-10x-x-109">N</span><span
+class="cmmi-10x-x-109">> b</span><sub><span
+class="cmr-8">1</span></sub>
+<span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub>
+<!--l. 20--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+
+
+
+<!--l. 20--><p class="indent" > Compute and print the stationary distribution of additive, multiplicative and
+intensive biased walks in a multiplex with 2 layers. Files <span
+class="cmti-10x-x-109">layer1</span>, <span
+class="cmti-10x-x-109">layer2</span>,
+contain the (undirected) edge list of the two layer, and each line is in the
+format:
+<!--l. 20--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 20--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 20--><p class="indent" > The file <span
+class="cmti-10x-x-109">overlapping network </span>has also a third column indicating the number of
+times two nodes are connected across all layers.
+<!--l. 20--><p class="indent" > <span
+class="cmmi-10x-x-109">N </span>is the number of nodes, <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> is the first bias exponent (the bias exponent
+for layer 1 for additive and multiplicative walks, the bias exponent on
+the participation coefficient for intensive walks), <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub> is the second bias
+exponent (the bias exponent for layer 1 for additive and multiplicative
+walks, the bias exponent on the participation coefficient for intensive
+walks).
+<!--l. 22--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 22--><p class="indent" > N lines. In the n-th line we report the node ID, the stationary distribution of
+that node for additive walks with exponents <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> and <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub>, the stationary distribution
+for multiplicative walks with exponents <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> and <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub>, the stationary distribution for
+multiplicative walks with exponents <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> and <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub>, the values of the bias exponents <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub>
+and <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub>.
+<!--l. 24--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 24--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, <span
+class="cmti-10x-x-109">“Biased random walks on multiplex</span>
+<span
+class="cmti-10x-x-109">networks”</span>, arxiv:1505.01378 (2015).
+<!--l. 24--><p class="indent" > Link to paper: <a
+href="http://arxiv.org/abs/1505.01378" class="url" ><span
+class="cmtt-10x-x-109">http://arxiv.org/abs/1505.01378</span></a>
+
+
+
+ <!--l. 259--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu56.html" >next</a>] [<a
+href="mammult_docsu54.html" >prev</a>] [<a
+href="mammult_docsu54.html#tailmammult_docsu54.html" >prev-tail</a>] [<a
+href="mammult_docsu55.html" >front</a>] [<a
+href="mammult_docsu54.html#mammult_docsu55.html" >up</a>] </p></div>
+<!--l. 259--><p class="indent" > <a
+ id="tailmammult_docsu55.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu56.html b/doc/html/mammult_docsu56.html
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--- /dev/null
+++ b/doc/html/mammult_docsu56.html
@@ -0,0 +1,43 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>Entropy rate</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
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+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 259--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu57.html" >next</a>] [<a
+href="mammult_docsu55.html" >prev</a>] [<a
+href="mammult_docsu55.html#tailmammult_docsu55.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu56.html">tail</a>] [<a
+href="mammult_docse7.html#mammult_docsu56.html" >up</a>] </p></div>
+ <h4 class="subsectionHead"><span class="titlemark">3.2.2 </span> <a
+ id="x67-660003.2.2"></a>Entropy rate</h4>
+<!--l. 7--><p class="noindent" >
+ <div class="subsubsectionTOCS">
+    <span class="subsubsectionToc" ><a
+href="mammult_docsu57.html#x68-670003.2.2"><span
+class="cmtt-10x-x-109">entropyrate2add</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu58.html#x69-680003.2.2"><span
+class="cmtt-10x-x-109">entropyrate2mult</span></a></span>
+<br />    <span class="subsubsectionToc" ><a
+href="mammult_docsu59.html#x70-690003.2.2"><span
+class="cmtt-10x-x-109">entropyrate2int</span></a></span>
+ </div>
+
+<!--l. 265--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu57.html" >next</a>] [<a
+href="mammult_docsu55.html" >prev</a>] [<a
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+href="mammult_docse7.html#mammult_docsu56.html" >up</a>] </p></div>
+<!--l. 265--><p class="indent" > <a
+ id="tailmammult_docsu56.html"></a>
+</body></html>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>3.2.2.0 entropyrate2add</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
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+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 7--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu58.html" >next</a>] [<a
+href="mammult_docsu56.html" >prev</a>] [<a
+href="mammult_docsu56.html#tailmammult_docsu56.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu57.html">tail</a>] [<a
+href="mammult_docsu56.html#mammult_docsu57.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x68-670003.2.2"></a><span
+class="cmtt-10x-x-109">entropyrate2add</span></h5>
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">entropyrate2add </span>- compute the entropy rate of additive biased walks in a
+multiplex with 2 layers.
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">entropyrate2add </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> < overlappingnetwork > <</span><span
+class="cmitt-10x-x-109">N</span><span
+class="cmmi-10x-x-109">></span>
+<span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub>
+<!--l. 20--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 20--><p class="indent" > Compute and print the entropy rate of an additive biased walk in a
+multiplex with 2 layers and bias parameters <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> and <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub>. Files <span
+class="cmti-10x-x-109">layer1</span>, <span
+class="cmti-10x-x-109">layer2</span>,
+contain the (undirected) edge list of the two layer, and each line is in the
+format:
+<!--l. 20--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 20--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 20--><p class="indent" > The file <span
+class="cmti-10x-x-109">overlapping network </span>has also a third column indicating the number of
+times two nodes are connected across all layers.
+<!--l. 20--><p class="indent" > <span
+class="cmmi-10x-x-109">N </span>is the number of nodes, <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> is the degree-biased exponent for layer 1, <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub> is
+the degree-biased exponent for layer 2.
+<!--l. 22--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 22--><p class="indent" > One line, reporting the value of the entropy rate <span
+class="cmmi-10x-x-109">h </span>of an additive biased
+random walks with <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> and <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub> as bias exponents, <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> and <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub>.
+
+
+
+<!--l. 24--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 24--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, <span
+class="cmti-10x-x-109">“Biased random walks on multiplex</span>
+<span
+class="cmti-10x-x-109">networks”</span>, arxiv:1505.01378 (2015).
+<!--l. 24--><p class="indent" > Link to paper: <a
+href="http://arxiv.org/abs/1505.01378" class="url" ><span
+class="cmtt-10x-x-109">http://arxiv.org/abs/1505.01378</span></a>
+
+
+
+ <!--l. 7--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu58.html" >next</a>] [<a
+href="mammult_docsu56.html" >prev</a>] [<a
+href="mammult_docsu56.html#tailmammult_docsu56.html" >prev-tail</a>] [<a
+href="mammult_docsu57.html" >front</a>] [<a
+href="mammult_docsu56.html#mammult_docsu57.html" >up</a>] </p></div>
+<!--l. 7--><p class="indent" > <a
+ id="tailmammult_docsu57.html"></a>
+</body></html>
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new file mode 100644
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+++ b/doc/html/mammult_docsu58.html
@@ -0,0 +1,109 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>3.2.2.0 entropyrate2mult</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 7--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu59.html" >next</a>] [<a
+href="mammult_docsu57.html" >prev</a>] [<a
+href="mammult_docsu57.html#tailmammult_docsu57.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu58.html">tail</a>] [<a
+href="mammult_docsu56.html#mammult_docsu58.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x69-680003.2.2"></a><span
+class="cmtt-10x-x-109">entropyrate2mult</span></h5>
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">entropyrate2mult </span>- compute the entropy rate of multiplicative biased walks
+in a multiplex with 2 layers.
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">entropyrate2mult </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> < overlappingnetwork > <</span><span
+class="cmitt-10x-x-109">N</span><span
+class="cmmi-10x-x-109">></span>
+<span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub>
+<!--l. 20--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 20--><p class="indent" > Compute and print the entropy rate of a multiplicative biased walk in a
+multiplex with 2 layers and bias parameters <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> and <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub>. Files <span
+class="cmti-10x-x-109">layer1</span>, <span
+class="cmti-10x-x-109">layer2</span>,
+contain the (undirected) edge list of the two layer, and each line is in the
+format:
+<!--l. 20--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 20--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 20--><p class="indent" > The file <span
+class="cmti-10x-x-109">overlapping network </span>has also a third column indicating the number of
+times two nodes are connected across all layers.
+<!--l. 20--><p class="indent" > <span
+class="cmmi-10x-x-109">N </span>is the number of nodes, <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> is the degree-biased exponent for layer 1, <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub> is
+the degree-biased exponent for layer 2.
+<!--l. 22--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 22--><p class="indent" > One line, reporting the value of the entropy rate <span
+class="cmmi-10x-x-109">h </span>of an multiplicative biased
+random walks with <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> and <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub> as bias exponents, <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">1</span></sub> and <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub>.
+<!--l. 24--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 24--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, <span
+class="cmti-10x-x-109">“Biased random walks on multiplex</span>
+<span
+class="cmti-10x-x-109">networks”</span>, arxiv:1505.01378 (2015).
+<!--l. 24--><p class="indent" > Link to paper: <a
+href="http://arxiv.org/abs/1505.01378" class="url" ><span
+class="cmtt-10x-x-109">http://arxiv.org/abs/1505.01378</span></a>
+
+
+
+ <!--l. 7--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu59.html" >next</a>] [<a
+href="mammult_docsu57.html" >prev</a>] [<a
+href="mammult_docsu57.html#tailmammult_docsu57.html" >prev-tail</a>] [<a
+href="mammult_docsu58.html" >front</a>] [<a
+href="mammult_docsu56.html#mammult_docsu58.html" >up</a>] </p></div>
+<!--l. 7--><p class="indent" > <a
+ id="tailmammult_docsu58.html"></a>
+</body></html>
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+++ b/doc/html/mammult_docsu59.html
@@ -0,0 +1,103 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>3.2.2.0 entropyrate2int</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 7--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu58.html" >prev</a>] [<a
+href="mammult_docsu58.html#tailmammult_docsu58.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu59.html">tail</a>] [<a
+href="mammult_docsu56.html#mammult_docsu59.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x70-690003.2.2"></a><span
+class="cmtt-10x-x-109">entropyrate2int</span></h5>
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">entropyrate2int </span>- compute the entropy rate of intensive biased walks in a
+multiplex with 2 layers.
+<!--l. 7--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 7--><p class="indent" > <span
+class="cmbx-10x-x-109">entropyrate2int </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> < overlappingnetwork > <</span><span
+class="cmitt-10x-x-109">N</span><span
+class="cmmi-10x-x-109">> b</span><sub><span
+class="cmr-8">1</span></sub>
+<span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmr-8">2</span></sub>
+<!--l. 20--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 20--><p class="indent" > Compute and print the entropy rate of an intensive biased walks in a
+multiplex with 2 layers and bias parameters <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmmi-8">p</span></sub> and <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmmi-8">o</span></sub>. Files <span
+class="cmti-10x-x-109">layer1</span>, <span
+class="cmti-10x-x-109">layer2</span>,
+contain the (undirected) edge list of the two layer, and each line is in the
+format:
+<!--l. 20--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 20--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 20--><p class="indent" > The file <span
+class="cmti-10x-x-109">overlapping network </span>has also a third column indicating the number of
+times two nodes are connected across all layers.
+<!--l. 20--><p class="indent" > <span
+class="cmmi-10x-x-109">N </span>is the number of nodes, <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmmi-8">p</span></sub> is the biased exponent on the participation
+coefficient, <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmmi-8">o</span></sub> is the biased exponent on the overlapping degree.
+<!--l. 22--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 22--><p class="indent" > One line, reporting the value of the entropy rate <span
+class="cmmi-10x-x-109">h </span>of an intensive biased
+random walks with <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmmi-8">p</span></sub> and <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmmi-8">o</span></sub> as bias exponents, <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmmi-8">p</span></sub> and <span
+class="cmmi-10x-x-109">b</span><sub><span
+class="cmmi-8">o</span></sub>.
+<!--l. 24--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 24--><p class="indent" > F. Battiston, V. Nicosia, V. Latora, <span
+class="cmti-10x-x-109">“Biased random walks on multiplex</span>
+<span
+class="cmti-10x-x-109">networks”</span>, arxiv:1505.01378 (2015).
+<!--l. 24--><p class="indent" > Link to paper: <a
+href="http://arxiv.org/abs/1505.01378" class="url" ><span
+class="cmtt-10x-x-109">http://arxiv.org/abs/1505.01378</span></a>
+ <!--l. 265--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu58.html" >prev</a>] [<a
+href="mammult_docsu58.html#tailmammult_docsu58.html" >prev-tail</a>] [<a
+href="mammult_docsu59.html" >front</a>] [<a
+href="mammult_docsu56.html#mammult_docsu59.html" >up</a>] </p></div>
+<!--l. 265--><p class="indent" > <a
+ id="tailmammult_docsu59.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu6.html b/doc/html/mammult_docsu6.html
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index 0000000..1c83cb0
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+++ b/doc/html/mammult_docsu6.html
@@ -0,0 +1,101 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.1.0 multiplexity.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu7.html" >next</a>] [<a
+href="mammult_docsu5.html" >prev</a>] [<a
+href="mammult_docsu5.html#tailmammult_docsu5.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu6.html">tail</a>] [<a
+href="mammult_docsu1.html#mammult_docsu6.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x9-80001.1.1"></a><span
+class="cmtt-10x-x-109">multiplexity.py</span></h5>
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">multiplexity.py </span>- compute the pairwise multiplexity between all the pairs of
+layers of a multiplex.
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">multiplexity.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer3</span><span
+class="cmmi-10x-x-109">></span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 17--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 17--><p class="indent" > Compute and print on output the pairwise multiplexity <span
+class="cmmi-10x-x-109">Q</span><sub><span
+class="cmmi-8">α,β</span></sub> (i.e., the
+fraction of nodes active on both layers) between all pairs of layers. The layers are
+given as input in the files <span
+class="cmti-10x-x-109">layer1</span>, <span
+class="cmti-10x-x-109">layer2</span>, etc.
+<!--l. 17--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
+in the format:
+<!--l. 17--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 17--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 28--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 28--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines, in the format:
+<!--l. 28--><p class="indent" >   <span
+class="cmti-10x-x-109">layer1 layer2 mult</span>
+<!--l. 28--><p class="noindent" >where <span
+class="cmti-10x-x-109">layer1 </span>and <span
+class="cmti-10x-x-109">layer2 </span>are the IDs of the layers, and <span
+class="cmti-10x-x-109">mult </span>is the value of the
+multiplexity <span
+class="cmmi-10x-x-109">Q</span><sub><span
+class="cmmi-8">layer</span><span
+class="cmr-8">1</span><span
+class="cmmi-8">,layer</span><span
+class="cmr-8">2</span></sub>. Layers IDs start from zero, are are associated to the
+layers in the same order in which the layer files are provided on the command
+line.
+<!--l. 30--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 30--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 30--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu7.html" >next</a>] [<a
+href="mammult_docsu5.html" >prev</a>] [<a
+href="mammult_docsu5.html#tailmammult_docsu5.html" >prev-tail</a>] [<a
+href="mammult_docsu6.html" >front</a>] [<a
+href="mammult_docsu1.html#mammult_docsu6.html" >up</a>] </p></div>
+<!--l. 4--><p class="indent" > <a
+ id="tailmammult_docsu6.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu7.html b/doc/html/mammult_docsu7.html
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+++ b/doc/html/mammult_docsu7.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.1.0 hamming_dist.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu8.html" >next</a>] [<a
+href="mammult_docsu6.html" >prev</a>] [<a
+href="mammult_docsu6.html#tailmammult_docsu6.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu7.html">tail</a>] [<a
+href="mammult_docsu1.html#mammult_docsu7.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x10-90001.1.1"></a><span
+class="cmtt-10x-x-109">hamming</span><span
+class="cmtt-10x-x-109">_dist.py</span></h5>
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">hamming</span><span
+class="cmbx-10x-x-109">_dist.py </span>- compute the normalised Hamming distance between all
+the pairs of layers of a multiplex.
+<!--l. 4--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 4--><p class="indent" > <span
+class="cmbx-10x-x-109">hamming</span><span
+class="cmbx-10x-x-109">_dist.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> <</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer3</span><span
+class="cmmi-10x-x-109">></span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 18--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 18--><p class="indent" > Compute and print on output the normalised Hamming distance <span
+class="cmmi-10x-x-109">H</span><sub><span
+class="cmmi-8">α,β</span></sub> (i.e.,
+the fraction of nodes which are active on either of the layers, but not on both)
+between all pairs of layers. The layers are given as input in the files <span
+class="cmti-10x-x-109">layer1</span>,
+<span
+class="cmti-10x-x-109">layer2</span>, etc.
+<!--l. 18--><p class="indent" > Each input file contains the (undirected) edge list of a layer, and each line is
+in the format:
+<!--l. 18--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 18--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 29--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 29--><p class="indent" > The program prints on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines, in the format:
+<!--l. 29--><p class="indent" >   <span
+class="cmti-10x-x-109">layer1 layer2 hamm</span>
+<!--l. 29--><p class="noindent" >where <span
+class="cmti-10x-x-109">layer1 </span>and <span
+class="cmti-10x-x-109">layer2 </span>are the IDs of the layers, and <span
+class="cmti-10x-x-109">hamm </span>is the value of the
+normalised Haming distance <span
+class="cmmi-10x-x-109">H</span><sub><span
+class="cmmi-8">layer</span><span
+class="cmr-8">1</span><span
+class="cmmi-8">,layer</span><span
+class="cmr-8">2</span></sub>. Layers IDs start from zero, are are
+associated to the layers in the same order in which the layer files are provided on
+the command line.
+<!--l. 31--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 31--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 31--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu8.html" >next</a>] [<a
+href="mammult_docsu6.html" >prev</a>] [<a
+href="mammult_docsu6.html#tailmammult_docsu6.html" >prev-tail</a>] [<a
+href="mammult_docsu7.html" >front</a>] [<a
+href="mammult_docsu1.html#mammult_docsu7.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu7.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu8.html b/doc/html/mammult_docsu8.html
new file mode 100644
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--- /dev/null
+++ b/doc/html/mammult_docsu8.html
@@ -0,0 +1,109 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.1.0 node_degree_vectors.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu9.html" >next</a>] [<a
+href="mammult_docsu7.html" >prev</a>] [<a
+href="mammult_docsu7.html#tailmammult_docsu7.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu8.html">tail</a>] [<a
+href="mammult_docsu1.html#mammult_docsu8.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x11-100001.1.1"></a><span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_degree</span><span
+class="cmtt-10x-x-109">_vectors.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">node</span><span
+class="cmbx-10x-x-109">_degree</span><span
+class="cmbx-10x-x-109">_vectors.py </span>- compute the degree vectors of all the nodes of a
+multiplex network
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">node</span><span
+class="cmbx-10x-x-109">_degree</span><span
+class="cmbx-10x-x-109">_vectors.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer1</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">[</span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">layer2</span><span
+class="cmmi-10x-x-109">> </span><span
+class="cmitt-10x-x-109">...]</span>
+<!--l. 15--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 15--><p class="indent" > Compute and print on output the degree vectors of all the nodes of a
+multiplex network, whose layers are given as input in the files <span
+class="cmti-10x-x-109">layer1</span>, <span
+class="cmti-10x-x-109">layer2</span>,
+etc.
+<!--l. 15--><p class="indent" > Each file contains the (undirected) edge list of a layer, and each line is in the
+format:
+<!--l. 15--><p class="indent" >   <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID dest</span><span
+class="cmti-10x-x-109">_ID</span>
+<!--l. 15--><p class="indent" > where <span
+class="cmti-10x-x-109">src</span><span
+class="cmti-10x-x-109">_ID </span>and <span
+class="cmti-10x-x-109">dest</span><span
+class="cmti-10x-x-109">_ID </span>are the IDs of the two endpoints of an
+edge.
+<!--l. 27--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 27--><p class="indent" > A list of lines, where the n-th line is the vector of degrees of the n-th node, in
+the format:
+<!--l. 27--><p class="indent" >   <span
+class="cmti-10x-x-109">noden</span><span
+class="cmti-10x-x-109">_deg</span><span
+class="cmti-10x-x-109">_lay1 noden</span><span
+class="cmti-10x-x-109">_deg</span><span
+class="cmti-10x-x-109">_lay2 ... noden</span><span
+class="cmti-10x-x-109">_deg</span><span
+class="cmti-10x-x-109">_layM</span>
+<!--l. 27--><p class="noindent" >As usual, node IDs start from zero and proceed sequentially, without gaps, i.e., if
+a node ID is not present in any of the layer files given as input, the program
+considers it as being isolated on all the layers.
+<!--l. 29--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 29--><p class="indent" > V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. Lett. </span><span
+class="cmbx-10x-x-109">111</span>, 058701 (2013).
+<!--l. 29--><p class="indent" > Link to paper: <a
+href="http://prl.aps.org/abstract/PRL/v111/i5/e058701" class="url" ><span
+class="cmtt-10x-x-109">http://prl.aps.org/abstract/PRL/v111/i5/e058701</span></a>
+<br
+class="newline" /><br
+class="newline" /> F. Battiston, V. Nicosia, V. Latora, “Structural measures for multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">89</span>, 032804 (2014).
+<!--l. 29--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804</span></a>
+
+
+
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu9.html" >next</a>] [<a
+href="mammult_docsu7.html" >prev</a>] [<a
+href="mammult_docsu7.html#tailmammult_docsu7.html" >prev-tail</a>] [<a
+href="mammult_docsu8.html" >front</a>] [<a
+href="mammult_docsu1.html#mammult_docsu8.html" >up</a>] </p></div>
+<!--l. 3--><p class="indent" > <a
+ id="tailmammult_docsu8.html"></a>
+</body></html>
diff --git a/doc/html/mammult_docsu9.html b/doc/html/mammult_docsu9.html
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--- /dev/null
+++ b/doc/html/mammult_docsu9.html
@@ -0,0 +1,97 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
+ "http://www.w3.org/TR/html4/loose.dtd">
+<html >
+<head><title>1.1.1.0 degs_to_binary.py</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+<meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/)">
+<!-- html,index=2,3,4,5,next -->
+<meta name="src" content="mammult_doc.tex">
+<meta name="date" content="2015-10-19 16:26:00">
+<link rel="stylesheet" type="text/css" href="mammult_doc.css">
+</head><body
+>
+ <!--l. 3--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu10.html" >next</a>] [<a
+href="mammult_docsu8.html" >prev</a>] [<a
+href="mammult_docsu8.html#tailmammult_docsu8.html" >prev-tail</a>] [<a
+href="#tailmammult_docsu9.html">tail</a>] [<a
+href="mammult_docsu1.html#mammult_docsu9.html" >up</a>] </p></div>
+ <h5 class="subsubsectionHead"><a
+ id="x12-110001.1.1"></a><span
+class="cmtt-10x-x-109">degs</span><span
+class="cmtt-10x-x-109">_to</span><span
+class="cmtt-10x-x-109">_binary.py</span></h5>
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">NAME</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">degs</span><span
+class="cmbx-10x-x-109">_to</span><span
+class="cmbx-10x-x-109">_binary.py </span>- compute the activity vectors of all the nodes of a
+multiplex.
+<!--l. 3--><p class="noindent" ><span
+class="cmbx-10x-x-109">SYNOPSYS</span>
+<!--l. 3--><p class="indent" > <span
+class="cmbx-10x-x-109">degs</span><span
+class="cmbx-10x-x-109">_to</span><span
+class="cmbx-10x-x-109">_binary.py </span><span
+class="cmmi-10x-x-109"><</span><span
+class="cmitt-10x-x-109">degree</span><span
+class="cmitt-10x-x-109">_vectors</span><span
+class="cmmi-10x-x-109">></span>
+<!--l. 14--><p class="noindent" ><span
+class="cmbx-10x-x-109">DESCRIPTION</span>
+<!--l. 14--><p class="indent" > Take a file which contains, on the n-th line, the degrees at each layer of the
+n-th node, (e.g., the result of the script <span
+class="cmtt-10x-x-109">node</span><span
+class="cmtt-10x-x-109">_degree</span><span
+class="cmtt-10x-x-109">_vectors.py</span>), in the
+format:
+<!--l. 14--><p class="indent" >   <span
+class="cmti-10x-x-109">noden</span><span
+class="cmti-10x-x-109">_deg</span><span
+class="cmti-10x-x-109">_lay1 noden</span><span
+class="cmti-10x-x-109">_deg</span><span
+class="cmti-10x-x-109">_lay2 ... noden</span><span
+class="cmti-10x-x-109">_deg</span><span
+class="cmti-10x-x-109">_layM</span>
+<!--l. 14--><p class="noindent" >and compute the corresponding node activity bit-strings, where a ”1”
+signals the presence of the node on that layer, while a zero indicates its
+absence.
+<!--l. 27--><p class="noindent" ><span
+class="cmbx-10x-x-109">OUTPUT</span>
+<!--l. 27--><p class="indent" > The program returns on <span
+class="cmtt-10x-x-109">stdout </span>a list of lines, where the n-th line is the
+activity bit-string of the n-th node. Additionally, the program prints on <span
+class="cmtt-10x-x-109">stderr</span>
+the distribution of all activity bit-strings, in the format:
+<!--l. 27--><p class="indent" >   <span
+class="cmti-10x-x-109">Bn Bit-string count</span>
+<!--l. 27--><p class="noindent" >Where <span
+class="cmti-10x-x-109">B </span>is the number of ones in the activity bit-string (i.e., the node-activity
+associated to that activity bit-string), <span
+class="cmti-10x-x-109">Bit-string </span>is the activity bit-string and
+<span
+class="cmti-10x-x-109">count </span>is the number of times that particular activity bit-string appears in the
+multiplex.
+<!--l. 31--><p class="noindent" ><span
+class="cmbx-10x-x-109">REFERENCE</span>
+<!--l. 31--><p class="indent" > V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex
+networks”, <span
+class="cmti-10x-x-109">Phys. Rev. E </span><span
+class="cmbx-10x-x-109">92</span>, 032805 (2015).
+<!--l. 31--><p class="indent" > Link to paper: <a
+href="http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805" class="url" ><span
+class="cmtt-10x-x-109">http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805</span></a>
+
+
+
+ <!--l. 4--><div class="crosslinks"><p class="noindent">[<a
+href="mammult_docsu10.html" >next</a>] [<a
+href="mammult_docsu8.html" >prev</a>] [<a
+href="mammult_docsu8.html#tailmammult_docsu8.html" >prev-tail</a>] [<a
+href="mammult_docsu9.html" >front</a>] [<a
+href="mammult_docsu1.html#mammult_docsu9.html" >up</a>] </p></div>
+<!--l. 4--><p class="indent" > <a
+ id="tailmammult_docsu9.html"></a>
+</body></html>
diff --git a/doc/latex/latex/dynamics/Ising/multiplex_ising.tex b/doc/latex/latex/dynamics/Ising/multiplex_ising.tex
new file mode 100644
index 0000000..ec87454
--- /dev/null
+++ b/doc/latex/latex/dynamics/Ising/multiplex_ising.tex
@@ -0,0 +1,22 @@
+%%%
+%%% Layer activity
+%%%
+
+\myprogram{{multiplex\_ising}}
+ {compute the coupled ising model in a multiplex with $2$ layers.}
+ {$<$layer1$>$ $<$layer2$>$ $<$T$>$ $<$J$>$ $<\gamma>$ $<h^{[1]}>$ $<h^{[2]}>$ $<p_1>$ $<p_2>$ $<num epochs>$}
+
+\mydescription{Compute and print the output of the ising dynamics on two coupled layers of a multiplex network.
+ Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each
+ line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.
+
+ $T$ is the value of thermal noise in the system, $J$ the value of peer pressure, $\gamma$ the relative ratio between internal coupling and peer pressure, $h^{[1]}$ and $h^{[2]}$ the external fields acting on the two layers, $p_1$ the probability for a spin on layer $1$ at $t=0$ to be up, $p_2$ the same probability for spins on layer $2$, $num epochs$ the number of epochs for the simulation.}
+
+\myreturn{One line, reporting all controlling parameter, the value of consensus in layer $1$ $m^{[1]}$, the value of consensus in layer $2$ $m^{[2]}$ and the coherence $C$.}
+
+\myreference{\refising}
diff --git a/doc/latex/latex/dynamics/randomwalks/entropyrate2add.tex b/doc/latex/latex/dynamics/randomwalks/entropyrate2add.tex
new file mode 100644
index 0000000..98a432b
--- /dev/null
+++ b/doc/latex/latex/dynamics/randomwalks/entropyrate2add.tex
@@ -0,0 +1,24 @@
+%%%
+%%% Layer activity
+%%%
+
+\myprogram{{entropyrate2add}}
+ {compute the entropy rate of additive biased walks in a multiplex with $2$ layers.}
+ {$<$layer1$>$ $<$layer2$>$ $<overlapping network>$ $<$N$>$ $b_1$ $b_2$}
+
+\mydescription{Compute and print the entropy rate of an additive biased walk in a multiplex with $2$ layers and bias parameters $b_1$ and $b_2$.
+ Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each
+ line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.
+
+ The file \textit{overlapping network} has also a third column indicating the number of times two nodes are connected across all layers.
+
+ $N$ is the number of nodes, $b_1$ is the degree-biased exponent for layer $1$, $b_2$ is the degree-biased exponent for layer $2$.}
+
+\myreturn{One line, reporting the value of the entropy rate $h$ of an additive biased random walks with $b_1$ and $b_2$ as bias exponents, $b_1$ and $b_2$.}
+
+\myreference{\refbiased}
diff --git a/doc/latex/latex/dynamics/randomwalks/entropyrate2int.tex b/doc/latex/latex/dynamics/randomwalks/entropyrate2int.tex
new file mode 100644
index 0000000..8a337f4
--- /dev/null
+++ b/doc/latex/latex/dynamics/randomwalks/entropyrate2int.tex
@@ -0,0 +1,24 @@
+%%%
+%%% Layer activity
+%%%
+
+\myprogram{{entropyrate2int}}
+ {compute the entropy rate of intensive biased walks in a multiplex with $2$ layers.}
+ {$<$layer1$>$ $<$layer2$>$ $<overlapping network>$ $<$N$>$ $b_1$ $b_2$}
+
+\mydescription{Compute and print the entropy rate of an intensive biased walks in a multiplex with $2$ layers and bias parameters $b_p$ and $b_o$.
+ Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each
+ line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.
+
+ The file \textit{overlapping network} has also a third column indicating the number of times two nodes are connected across all layers.
+
+ $N$ is the number of nodes, $b_p$ is the biased exponent on the participation coefficient, $b_o$ is the biased exponent on the overlapping degree.}
+
+\myreturn{One line, reporting the value of the entropy rate $h$ of an intensive biased random walks with $b_p$ and $b_o$ as bias exponents, $b_p$ and $b_o$.}
+
+\myreference{\refbiased}
diff --git a/doc/latex/latex/dynamics/randomwalks/entropyrate2mult.tex b/doc/latex/latex/dynamics/randomwalks/entropyrate2mult.tex
new file mode 100644
index 0000000..7abfecd
--- /dev/null
+++ b/doc/latex/latex/dynamics/randomwalks/entropyrate2mult.tex
@@ -0,0 +1,24 @@
+%%%
+%%% Layer activity
+%%%
+
+\myprogram{{entropyrate2mult}}
+ {compute the entropy rate of multiplicative biased walks in a multiplex with $2$ layers.}
+ {$<$layer1$>$ $<$layer2$>$ $<overlapping network>$ $<$N$>$ $b_1$ $b_2$}
+
+\mydescription{Compute and print the entropy rate of a multiplicative biased walk in a multiplex with $2$ layers and bias parameters $b_1$ and $b_2$.
+ Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each
+ line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.
+
+ The file \textit{overlapping network} has also a third column indicating the number of times two nodes are connected across all layers.
+
+ $N$ is the number of nodes, $b_1$ is the degree-biased exponent for layer $1$, $b_2$ is the degree-biased exponent for layer $2$.}
+
+\myreturn{One line, reporting the value of the entropy rate $h$ of an multiplicative biased random walks with $b_1$ and $b_2$ as bias exponents, $b_1$ and $b_2$.}
+
+\myreference{\refbiased}
diff --git a/doc/latex/latex/dynamics/randomwalks/statdistr2.tex b/doc/latex/latex/dynamics/randomwalks/statdistr2.tex
new file mode 100644
index 0000000..09c1bc2
--- /dev/null
+++ b/doc/latex/latex/dynamics/randomwalks/statdistr2.tex
@@ -0,0 +1,24 @@
+%%%
+%%% Layer activity
+%%%
+
+\myprogram{{statdistr2}}
+ {compute the stationary distribution of additive, multiplicative and intensive biased walks in a multiplex with $2$ layers.}
+ {$<$layer1$>$ $<$layer2$>$ $<overlapping network>$ $<$N$>$ $b_1$ $b_2$}
+
+\mydescription{Compute and print the stationary distribution of additive, multiplicative and intensive biased walks in a multiplex with $2$ layers.
+ Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each
+ line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.
+
+ The file \textit{overlapping network} has also a third column indicating the number of times two nodes are connected across all layers.
+
+ $N$ is the number of nodes, $b_1$ is the first bias exponent (the bias exponent for layer $1$ for additive and multiplicative walks, the bias exponent on the participation coefficient for intensive walks), $b_2$ is the second bias exponent (the bias exponent for layer $1$ for additive and multiplicative walks, the bias exponent on the participation coefficient for intensive walks).}
+
+\myreturn{N lines. In the n-th line we report the node ID, the stationary distribution of that node for additive walks with exponents $b_1$ and $b_2$, the stationary distribution for multiplicative walks with exponents $b_1$ and $b_2$, the stationary distribution for multiplicative walks with exponents $b_1$ and $b_2$, the values of the bias exponents $b_1$ and $b_2$.}
+
+\myreference{\refbiased}
diff --git a/doc/latex/latex/models/correlations/tune_qnn_adaptive.tex b/doc/latex/latex/models/correlations/tune_qnn_adaptive.tex
new file mode 100644
index 0000000..016b674
--- /dev/null
+++ b/doc/latex/latex/models/correlations/tune_qnn_adaptive.tex
@@ -0,0 +1,64 @@
+\myprogram{{tune\_qnn\_adaptive}}
+ {Construct a multiplex with prescribed inter-layer correlations.}
+ {$<$degs1$>$ $<$degs2$>$ $<$mu$>$ $<$eps$>$ $<$beta$>$ [RND|NAT|INV]}
+
+\mydescription{This programs tunes the inter-layer degree correlation
+ exponent $\mu$. If we consider two layers of a multiplex,
+ and we denote by $k$ the degree of a node on the first layer
+ and by $q$ the degree of the same node on the second layers,
+ the inter-layer degree correlation function is defined as:
+
+ \begin{equation*}
+ \overline{q}(k) = \sum_{q'} q' P(q'|k)
+ \end{equation*}
+
+ where $\overline{q}(k)$ is the average degree on layer $2$
+ of nodes having degree $k$ on layer $1$.
+
+ The program assumes that we want to set the degree
+ correlation function such that:
+
+ \begin{equation*}
+ \overline{q}(k) = a k^{\mu}
+ \end{equation*}
+
+ where the exponent of the power-law function is given by
+ the user (it is indeed the parameter \textit{mu}), and
+ successively adjusts the pairing between nodes at the two
+ layers in order to obtain a correlation function as close
+ as possible to the desired one. The files \textit{degs1}
+ and \textit{degs2} contain, respectively, the degrees of
+ the nodes on the first layer and on the second layer.
+
+ The parameter \textit{eps} is the accuracy of \textit{mu}.
+ For instance, if \textit{mu} is set equal to -0.25
+ and \textit{eps} is equal to 0.0001, the program stops when
+ the configuration of node pairing corresponds to a value of
+ the exponent $\mu$ which differs from -0.25 by less than
+ 0.0001.
+
+ The parameter \textit{beta} is the typical inverse
+ temperature of simulated annealing.
+
+ If no other parameter is specified, or if the last parameter
+ is \texttt{RND}, the program starts from a random pairing of
+ nodes. If the last parameter is \texttt{NAT} then the
+ program assumes that the initial pairing is the natural one,
+ where the nodes have the same ID on both layers. Finally,
+ if \texttt{INV} is specified, the initial pairing is the
+ inverse pairing, i.e. the one where node 0 on layer 1 is
+ paired with node N-1 on layer 2, and so on.
+
+ }
+
+
+\myreturn{The program prints on \texttt{stdout} a pairing, i.e. a list
+of lines in the format:
+
+\hspace{0.5cm} \textit{IDL1 IDL2}
+
+where \textit{IDL1} is the ID of the node on layer 1 and \textit{IDL2}
+is the corresponding ID of the same node on layer 2.
+}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/models/correlations/tune_rho.tex b/doc/latex/latex/models/correlations/tune_rho.tex
new file mode 100644
index 0000000..27b6079
--- /dev/null
+++ b/doc/latex/latex/models/correlations/tune_rho.tex
@@ -0,0 +1,45 @@
+\myprogram{{tune\_rho}}
+ {Construct a multiplex with prescribed inter-layer correlations.}
+ {$<$rank1$>$ $<$rank2$>$ $<$rho$>$ $<$eps$>$ $<$beta$>$ [RND|NAT|INV]}
+
+\mydescription{This programs tunes the inter-layer degree correlation
+ coefficient $\rho$ (Spearman's rank correlation) of two
+ layers, by adjusting the inter-layer pairing of nodes. The
+ files \textit{rank1} and \textit{rank2} are the rankings of
+ nodes in the first and second layer, where the n-th line of
+ the file contains the rank of the n-th node (the highest
+ ranked node has rank equal to 1).
+
+ The parameter \textit{rho} is the desired value of the
+ Spearman's rank correlation coefficient, while \textit{eps}
+ is the accuracy of \textit{rho}. For instance,
+ if \textit{rho} is set equal to -0.25 and \textit{eps} is
+ equal to 0.0001, the program stops when the configuration of
+ node pairing corresponds to a value of $\rho$ which differs
+ from -0.25 by less than 0.0001.
+
+ The parameter \textit{beta} is the typical inverse
+ temperature of simulated annealing.
+
+ If no other parameter is specified, or if the last parameter
+ is \texttt{RND}, the program starts from a random pairing of
+ nodes. If the last parameter is \texttt{NAT} then the
+ program assumes that the initial pairing is the natural one,
+ where the nodes have the same ID on both layers. Finally,
+ if \texttt{INV} is specified, the initial pairing is the
+ inverse pairing, i.e. the one where node 0 on layer 1 is
+ paired with node N-1 on layer 2, and so on.
+
+ }
+
+
+\myreturn{The program prints on \texttt{stdout} a pairing, i.e. a list
+of lines in the format:
+
+\hspace{0.5cm} \textit{IDL1 IDL2}
+
+where \textit{IDL1} is the ID of the node on layer 1 and \textit{IDL2}
+is the corresponding ID of the same node on layer 2.
+}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/models/growth/nibilab_linear_delay.tex b/doc/latex/latex/models/growth/nibilab_linear_delay.tex
new file mode 100644
index 0000000..afbf083
--- /dev/null
+++ b/doc/latex/latex/models/growth/nibilab_linear_delay.tex
@@ -0,0 +1,67 @@
+\myprogram{{nibilab\_linear\_delay}}
+ {Multiplex linear preferential attachment model --
+ Asynchronous arrival.}
+ {$<$N$>$ $<$m$>$ $<$m0$>$ $<$outfile$>$ $<$a$>$ $<$b$>$
+ $<$c$>$ $<$d$>$ $<$beta$>$}
+
+\mydescription{Grow a two-layer multiplex network using the multiplex linear
+ preferential attachment model by Nicosia, Bianconi, Latora,
+ Barthelemy (NiBiLaB).
+
+ The probability for a newly arrived node $i$ to create a
+ link to node $j$ on layer $1$ is:
+
+ \begin{equation*}
+ \Pi_{i\to j}^{1} \propto ak\lay{1}_j + bk\lay{2}_j
+ \end{equation*}
+
+ and the dual probability for $i$ to create a link to $j$ on
+ layer $2$ is:
+
+ \begin{equation*}
+ \Pi_{i\to j}^{2} \propto ck\lay{1}_j + dk\lay{2}_j
+ \end{equation*}
+
+ Each new node arrives first on layer $1$, and its replica on
+ the layer $2$ appears after a time delay $\tau$ sampled from
+ the power-law function:
+
+ \begin{equation*}
+ P(\tau) \sim \tau^{-\beta}
+ \end{equation*}
+
+ The (mandatory) parameters are as follows:
+
+ \begin{itemize}
+
+ \item \textbf{N} number of nodes in the final graph
+
+ \item \textbf{m} number of new edges brought by each new node
+
+ \item \textbf{m0} number of nodes in the initial seed
+ graph. \textit{m0} must be larger than of equal
+ to \textit{m}.
+
+ \item \textbf{outfile} the name of the file which will contain the
+
+ \item \textbf{a,b,c,d} the coefficients of the attaching probability
+ function
+
+ \item \textbf{beta} the exponent of the power-law delay
+ function which determines the arrival of replicas on layer $2$
+
+ \end{itemize}
+ }
+
+
+\myreturn{The program dumps on the file \texttt{outfile} the
+ (undirected) edge list of the resulting network. Each line of the
+ file is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.
+}
+
+\myreference{\refgrowth}
diff --git a/doc/latex/latex/models/growth/nibilab_linear_delay_mix.tex b/doc/latex/latex/models/growth/nibilab_linear_delay_mix.tex
new file mode 100644
index 0000000..5863951
--- /dev/null
+++ b/doc/latex/latex/models/growth/nibilab_linear_delay_mix.tex
@@ -0,0 +1,68 @@
+\myprogram{{nibilab\_linear\_delay\_mix}}
+ {Multiplex linear preferential attachment model --
+ Asynchronous arrival and randomly selected first layer.}
+ {$<$N$>$ $<$m$>$ $<$m0$>$ $<$outfile$>$ $<$a$>$ $<$b$>$
+ $<$c$>$ $<$d$>$ $<$beta$>$}
+
+\mydescription{Grow a two-layer multiplex network using the multiplex linear
+ preferential attachment model by Nicosia, Bianconi, Latora,
+ Barthelemy (NiBiLaB).
+
+ The probability for a newly arrived node $i$ to create a
+ link to node $j$ on layer $1$ is:
+
+ \begin{equation*}
+ \Pi_{i\to j}^{1} \propto ak\lay{1}_j + bk\lay{2}_j
+ \end{equation*}
+
+ and the dual probability for $i$ to create a link to $j$ on
+ layer $2$ is:
+
+ \begin{equation*}
+ \Pi_{i\to j}^{2} \propto ck\lay{1}_j + dk\lay{2}_j
+ \end{equation*}
+
+ Each new node arrives on one of the two layers, chosen
+ uniformly at random, and its replica on the other layer
+ appears after a time delay $\tau$ sampled from the power-law
+ function:
+
+ \begin{equation*}
+ P(\tau) \sim \tau^{-\beta}
+ \end{equation*}
+
+ The (mandatory) parameters are as follows:
+
+ \begin{itemize}
+
+ \item \textbf{N} number of nodes in the final graph
+
+ \item \textbf{m} number of new edges brought by each new node
+
+ \item \textbf{m0} number of nodes in the initial seed
+ graph. \textit{m0} must be larger than of equal
+ to \textit{m}.
+
+ \item \textbf{outfile} the name of the file which will contain the
+
+ \item \textbf{a,b,c,d} the coefficients of the attaching probability
+ function
+
+ \item \textbf{beta} the exponent of the power-law delay
+ function which determines the arrival of replicas on layer $2$
+
+ \end{itemize}
+ }
+
+
+\myreturn{The program dumps on the file \texttt{outfile} the
+ (undirected) edge list of the resulting network. Each line of the
+ file is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.
+}
+
+\myreference{\refgrowth}
diff --git a/doc/latex/latex/models/growth/nibilab_linear_delta.tex b/doc/latex/latex/models/growth/nibilab_linear_delta.tex
new file mode 100644
index 0000000..27ebbd0
--- /dev/null
+++ b/doc/latex/latex/models/growth/nibilab_linear_delta.tex
@@ -0,0 +1,57 @@
+\myprogram{{nibilab\_linear\_delta}}
+ {Multiplex linear preferential attachment model --
+ Synchronous arrival.}
+ {$<$N$>$ $<$m$>$ $<$m0$>$ $<$outfile$>$ $<$a$>$ $<$b$>$ $<$c$>$ $<$d$>$}
+
+\mydescription{Grow a two-layer multiplex network using the multiplex linear
+ preferential attachment model by Nicosia, Bianconi, Latora,
+ Barthelemy (NiBiLaB).
+
+ The probability for a newly arrived node $i$ to create a
+ link to node $j$ on layer $1$ is:
+
+ \begin{equation*}
+ \Pi_{i\to j}^{1} \propto ak\lay{1}_j + bk\lay{2}_j
+ \end{equation*}
+
+ and the dual probability for $i$ to create a link to $j$ on
+ layer $2$ is:
+
+ \begin{equation*}
+ \Pi_{i\to j}^{2} \propto ck\lay{1}_j + dk\lay{2}_j
+ \end{equation*}
+
+ Each new node arrives at the same time on both layers.
+
+ The (mandatory) parameters are as follows:
+
+ \begin{itemize}
+
+ \item \textbf{N} number of nodes in the final graph
+
+ \item \textbf{m} number of new edges brought by each new node
+
+ \item \textbf{m0} number of nodes in the initial seed
+ graph. \textit{m0} must be larger than of equal
+ to \textit{m}.
+
+ \item \textbf{outfile} the name of the file which will contain the
+
+ \item \textbf{a,b,c,d} the coefficients of the attaching probability
+ function
+
+ \end{itemize}
+ }
+
+
+\myreturn{The program dumps on the file \texttt{outfile} the
+ (undirected) edge list of the resulting network. Each line of the
+ file is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.
+}
+
+\myreference{\refgrowth}
diff --git a/doc/latex/latex/models/growth/nibilab_linear_random_times.tex b/doc/latex/latex/models/growth/nibilab_linear_random_times.tex
new file mode 100644
index 0000000..5f1c0fe
--- /dev/null
+++ b/doc/latex/latex/models/growth/nibilab_linear_random_times.tex
@@ -0,0 +1,63 @@
+\myprogram{{nibilab\_linear\_random\_times}}
+ {Multiplex linear preferential attachment model --
+ Asynchronous arrival with randomly sampled arrival times on
+ layer 2.}
+ {$<$N$>$ $<$m$>$ $<$m0$>$ $<$outfile$>$ $<$a$>$ $<$b$>$
+ $<$c$>$ $<$d$>$ }
+
+\mydescription{Grow a two-layer multiplex network using the multiplex linear
+ preferential attachment model by Nicosia, Bianconi, Latora,
+ Barthelemy (NiBiLaB).
+
+ The probability for a newly arrived node $i$ to create a
+ link to node $j$ on layer $1$ is:
+
+ \begin{equation*}
+ \Pi_{i\to j}^{1} \propto ak\lay{1}_j + bk\lay{2}_j
+ \end{equation*}
+
+ and the dual probability for $i$ to create a link to $j$ on
+ layer $2$ is:
+
+ \begin{equation*}
+ \Pi_{i\to j}^{2} \propto ck\lay{1}_j + dk\lay{2}_j
+ \end{equation*}
+
+ Each new node arrives on layer $1$, but its replica on the
+ other layer appears at a uniformly chosen random time in
+ $[m0+1; N]$.
+
+
+ The (mandatory) parameters are as follows:
+
+ \begin{itemize}
+
+ \item \textbf{N} number of nodes in the final graph
+
+ \item \textbf{m} number of new edges brought by each new node
+
+ \item \textbf{m0} number of nodes in the initial seed
+ graph. \textit{m0} must be larger than of equal
+ to \textit{m}.
+
+ \item \textbf{outfile} the name of the file which will contain the
+
+ \item \textbf{a,b,c,d} the coefficients of the attaching probability
+ function
+
+
+ \end{itemize}
+ }
+
+
+\myreturn{The program dumps on the file \texttt{outfile} the
+ (undirected) edge list of the resulting network. Each line of the
+ file is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.
+}
+
+\myreference{\refgrowth}
diff --git a/doc/latex/latex/models/growth/nibilab_nonlinear.tex b/doc/latex/latex/models/growth/nibilab_nonlinear.tex
new file mode 100644
index 0000000..2e48a18
--- /dev/null
+++ b/doc/latex/latex/models/growth/nibilab_nonlinear.tex
@@ -0,0 +1,60 @@
+\myprogram{{nibilab\_nonlinear}}
+ {Multiplex non-linear preferential attachment model --
+ Synchronous arrival.}
+ {$<$N$>$ $<$m$>$ $<$m0$>$ $<$outfile$>$ $<$alpha$>$ $<$beta$>$}
+
+\mydescription{Grow a two-layer multiplex network using the multiplex non-linear
+ preferential attachment model by Nicosia, Bianconi, Latora,
+ Barthelemy (NiBiLaB).
+
+ The probability for a newly arrived node $i$ to create a
+ link to node $j$ on layer $1$ is:
+
+ \begin{equation*}
+ \Pi_{i\to j}^{1} \propto \frac{\left(k\lay{1}_j\right)^{\alpha}}
+ {\left(k\lay{2}_j\right)^{\beta}}
+ \end{equation*}
+
+ and the dual probability for $i$ to create a link to $j$ on
+ layer $2$ is:
+
+ \begin{equation*}
+ \Pi_{i\to j}^{2} \propto \frac{\left(k\lay{2}_j\right)^{\alpha}}
+ {\left(k\lay{1}_j\right)^{\beta}}
+ \end{equation*}
+
+ Each node arrives simultaneously on both layers.
+
+
+ The (mandatory) parameters are as follows:
+
+ \begin{itemize}
+
+ \item \textbf{N} number of nodes in the final graph
+
+ \item \textbf{m} number of new edges brought by each new node
+
+ \item \textbf{m0} number of nodes in the initial seed
+ graph. \textit{m0} must be larger than of equal
+ to \textit{m}.
+
+ \item \textbf{outfile} the name of the file which will contain the
+
+ \item \textbf{alpha, beta} exponents of of the attaching probability
+ function
+
+ \end{itemize}
+ }
+
+
+\myreturn{The program dumps on the file \texttt{outfile} the
+ (undirected) edge list of the resulting network. Each line of the
+ file is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.
+}
+
+\myreference{\refgrowth}
diff --git a/doc/latex/latex/models/growth/node_deg_over_time.tex b/doc/latex/latex/models/growth/node_deg_over_time.tex
new file mode 100644
index 0000000..351045e
--- /dev/null
+++ b/doc/latex/latex/models/growth/node_deg_over_time.tex
@@ -0,0 +1,50 @@
+\myprogram{{node\_deg\_over\_time.py}}
+ {Time evolution of the degree of a node in a growing graph.}
+ {$<$layer$>$ $<$arrival\_times$>$ $<$node\_id$>$
+ [$<$node\_id$>$ ...]}
+
+\mydescription{Compute the degree $k_{i}(t)$ of node $i$ in a growing
+ network as a function of time. The file \textit{layer}
+ contains the edge list of the final network. Each line of
+ the file is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.
+
+ The file \textit{arrival\_times} is a list of node arrival times, in
+ the format:
+
+ \hspace{0.5cm} \textit{time\_i node\_i}
+
+ where \textit{time\_i} is the time at which \textit{node\_i} arrived
+ in the graph. Notice that \textit{time\_i} must be an integer in the
+ range [0, N-1], where N is the total number of nodes in the final
+ graph.
+
+ The third parameter \textit{node\_id} is the ID of the node whose
+ degree over time will be printed on output. If more than
+ one \textit{node\_id} is provided, the degrees over time of all the
+ corresponding nodes are printed on output.
+ }
+
+
+\myreturn{The program prints on \texttt{stdout} a list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{t kit}
+
+ where \textit{kit} is the degree of node \textit{i} at
+ time \textit{t}. The first line of output is in the format:
+
+ \hspace{0.5cm} \textit{\#\#\#\# node\_id}
+
+ where \textit{node\_id} is the ID of node \textit{i}.
+
+ If more than one \textit{node\_id}s is provided as input, the program
+ prints the degree over time of all of them, sequentially.
+
+}
+
+\myreference{\refgrowth}
diff --git a/doc/latex/latex/models/nullmodels/model_MDM.tex b/doc/latex/latex/models/nullmodels/model_MDM.tex
new file mode 100644
index 0000000..dd754b8
--- /dev/null
+++ b/doc/latex/latex/models/nullmodels/model_MDM.tex
@@ -0,0 +1,37 @@
+\myprogram{{model\_MDM.py}}
+ {Multi-activity Deterministic Model.}
+ {$<$Bi\_file$>$ $<$M$>$}
+
+\mydescription{This is the Multi-activity Deterministic Model (MDM).
+ In this model each node $i$ is considered active if it was
+ active in the reference multiplex, maintains the same value
+ of node activity $B_i$ (i.e., the number of layers in which
+ it was active) and is associated an activity vector sampled
+ uniformly at random from the $M\choose{B_i}$ possible
+ activity vectors with $B_i$ non-null entries.
+
+ The file \textit{Bi\_file} is in the format:
+
+ \hspace{0.5cm} \textit{Bi N(Bi)}
+
+ where \textit{Bi} is a value of node activity
+ and \textit{N(Bi)} is the number of nodes which had node
+ activity equaly to \textit{Bi} in the reference multiplex.
+
+ The parameter \textit{M} is the number of layers in the
+ multiplex.
+}
+
+
+\myreturn{The program prints on \texttt{stdout} a distribution of
+ bit-strings, in the format:
+
+ \hspace{0.5cm} \textit{Bi bitstring count}
+
+ where \textit{bitstring} is the activity
+ bitstring, \textit{Bi} is the number of non-zero entries
+ of \textit{bitstring} and \textit{count} is the number of
+ times that \textit{bitstrings} appear in the null model.}
+
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/models/nullmodels/model_MSM.tex b/doc/latex/latex/models/nullmodels/model_MSM.tex
new file mode 100644
index 0000000..e3c8abf
--- /dev/null
+++ b/doc/latex/latex/models/nullmodels/model_MSM.tex
@@ -0,0 +1,38 @@
+\myprogram{{model\_MSM.py}}
+ {Multi-activity Stochastic Model.}
+ {$<$node\_Bi\_file$>$ $<$M$>$}
+
+\mydescription{This is the Multi-activity Stochastic Model (MSM).
+ In this model each node $i$ is considered active if it was
+ active in the reference multiplex, and is activated on
+ each layer with a probability equal to $B_i/M$ where $B_i$
+ was the activity of node $i$ in the reference multiplex.
+
+ The file \textit{node\_Bi\_file} is in the format:
+
+ \hspace{0.5cm} \textit{node\_i Bi)}
+
+ where \textit{Bi} is the value of node activity
+ of \textit{node\_i} in the reference multiplex.
+
+
+ The parameter \textit{M} is the number of layers in the
+ multiplex.
+}
+
+\myreturn{The program prints on \texttt{stdout} a node-layer list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{node\_i layer\_i}
+
+ where \textit{node\_i} is the ID of a node and \textit{layre\_i} is
+ the ID of a layer. This list indicates which nodes are active in
+ which layer. For instance, the line:
+
+ \hspace{0.5cm} \textit{24 3}
+
+ indicates that the node with ID \textit{24} is active on
+ layer \textit{3}.
+}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/models/nullmodels/model_hypergeometric.tex b/doc/latex/latex/models/nullmodels/model_hypergeometric.tex
new file mode 100644
index 0000000..0315c7b
--- /dev/null
+++ b/doc/latex/latex/models/nullmodels/model_hypergeometric.tex
@@ -0,0 +1,33 @@
+\myprogram{{model\_hypergeometric.py}}
+ {Hypergeometric node activity null model.}
+ {$<$layer\_N\_file$>$ $<$N$>$}
+
+\mydescription{This is the hypergeometric model of node activation. In
+ this model each layer has exactly the same number of active
+ node of a reference multiplex network, but nodes on each
+ layer are activated uniformly at random, thus destroying all
+ inter-layer activity correlation patterns.
+
+ The file \textit{layer\_N\_file} reports on the n-th line
+ the number of active nodes on the n-th layer (starting from
+ zero). The second parameter \textit{N} is the total number
+ of active nodes in the multiplex.
+ }
+
+
+\myreturn{The program prints on \texttt{stdout} a node-layer list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{node\_i layer\_i}
+
+ where \textit{node\_i} is the ID of a node and \textit{layre\_i} is
+ the ID of a layer. This list indicates which nodes are active in
+ which layer. For instance, the line:
+
+ \hspace{0.5cm} \textit{24 3}
+
+ indicates that the node with ID \textit{24} is active on
+ layer \textit{3}.
+}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/models/nullmodels/model_layer_growth.tex b/doc/latex/latex/models/nullmodels/model_layer_growth.tex
new file mode 100644
index 0000000..9c0bb12
--- /dev/null
+++ b/doc/latex/latex/models/nullmodels/model_layer_growth.tex
@@ -0,0 +1,46 @@
+\myprogram{{model\_layer\_growth.py}}
+ {Layer growth with preferential activation model.}
+ {$<$layer\_N\_file$>$ $<$N$>$ $<$M0$>$ $<$A$>$ [RND]}
+
+\mydescription{This is the model of layer growth with preferential
+ node activation. In this model an entire new layer arrives
+ at time $t$ and a number of nodes $N_t$ is activated ($N\_t$
+ is equal to the number of nodes active on that layer in the
+ reference multiplex). Then, each node $i$ of the new layer
+ is activated with a probability:
+
+ \begin{equation*}
+ P_i(t) \propto A + B_i(t)
+ \end{equation*}
+
+ where $B_i(t)$ is the activity of node $i$ at time $t$
+ (i.e., the number of layers in which node $i$ is active at
+ time $t$) while $A>0$ is an intrinsic attractiveness.
+
+ The file \textit{layer\_N\_file} reports on the n-th line
+ the number of active nodes on the n-th layer.
+
+ The parameter \textit{N} is the number of nodes in the
+ multiplex, \textit{M0} is the number of layers in the
+ initial network, \textit{A} is the value of
+ node attractiveness.
+
+ If the user specifies \texttt{RND} as the last parameter,
+ the sequence of layers is }
+
+\myreturn{The program prints on \texttt{stdout} a node-layer list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{node\_i layer\_i}
+
+ where \textit{node\_i} is the ID of a node and \textit{layre\_i} is
+ the ID of a layer. This list indicates which nodes are active in
+ which layer. For instance, the line:
+
+ \hspace{0.5cm} \textit{24 3}
+
+ indicates that the node with ID \textit{24} is active on
+ layer \textit{3}.
+}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/structure/activity/degs_to_activity_overlap.tex b/doc/latex/latex/structure/activity/degs_to_activity_overlap.tex
new file mode 100644
index 0000000..6e1908f
--- /dev/null
+++ b/doc/latex/latex/structure/activity/degs_to_activity_overlap.tex
@@ -0,0 +1,29 @@
+\myprogram{{degs\_to\_activity\_overlap.py}}
+ {compute the activity and the total (overlapping) degree of
+ all the nodes of a multiplex.}
+ {$<$degree\_vectors$>$}
+
+\mydescription{Take a file which contains, on the n-th line, the degrees at each
+ layer of the n-th node, (e.g., the result of the
+ script \texttt{node\_degree\_vectors.py}), in the format:
+
+ \hspace{0.5cm}\textit{noden\_deg\_lay1 noden\_deg\_lay2 ... noden\_deg\_layM}
+
+ \noindent and compute the activity (i.e., the number of layers in
+ which a node is not isolated) and the total (overlapping) degree of
+ each node.}
+
+\myreturn{The program prints on \texttt{stdout} a list of lines, where
+ the n-th line contains the activity and the total degree of the n-th
+ nodem in the format:
+
+ \hspace{0.5cm}\textit{noden\_activity noden\_tot\_deg}
+
+ \noindent As usual, the program assumes that node IDs start from zero
+ and proceed sequentially, without gaps, i.e., if a node ID is not
+ present in any of the layer files given as input, the program
+ considers it as being isolated on all the layers.
+ }
+
+\myreference{\refcorrelations}
+
diff --git a/doc/latex/latex/structure/activity/degs_to_binary.tex b/doc/latex/latex/structure/activity/degs_to_binary.tex
new file mode 100644
index 0000000..7441b2d
--- /dev/null
+++ b/doc/latex/latex/structure/activity/degs_to_binary.tex
@@ -0,0 +1,32 @@
+\myprogram{{degs\_to\_binary.py}}
+ {compute the activity vectors of all the nodes of a multiplex.}
+ {$<$degree\_vectors$>$}
+
+\mydescription{Take a file which contains, on the n-th line, the degrees at each
+ layer of the n-th node, (e.g., the result of the
+ script \texttt{node\_degree\_vectors.py}), in the format:
+
+ \hspace{0.5cm}\textit{noden\_deg\_lay1 noden\_deg\_lay2 ... noden\_deg\_layM}
+
+ \noindent and compute the corresponding node activity bit-strings,
+ where a "1" signals the presence of the node on that layer, while a
+ zero indicates its absence.
+}
+
+\myreturn{The program returns on \texttt{stdout} a list of lines,
+ where the n-th line is the activity bit-string of the n-th
+ node. Additionally, the program prints on \texttt{stderr} the
+ distribution of all activity bit-strings, in the format:
+
+ \hspace{0.5cm}\textit{Bn Bit-string count}
+
+ \noindent Where \textit{B} is the number of ones in the activity
+ bit-string (i.e., the node-activity associated to that activity
+ bit-string), \textit{Bit-string} is the activity bit-string
+ and \textit{count} is the number of times that particular activity
+ bit-string appears in the multiplex.}
+
+
+
+\myreference{\refcorrelations}
+
diff --git a/doc/latex/latex/structure/activity/hamming_dist.tex b/doc/latex/latex/structure/activity/hamming_dist.tex
new file mode 100644
index 0000000..3af188f
--- /dev/null
+++ b/doc/latex/latex/structure/activity/hamming_dist.tex
@@ -0,0 +1,31 @@
+\myprogram{{hamming\_dist.py}}
+ {compute the normalised Hamming distance between all the pairs of
+ layers of a multiplex.}
+ {$<$layer1$>$ $<$layer2$>$ [$<$layer3$>$...]}
+
+\mydescription{Compute and print on output the normalised Hamming distance
+ $H_{\alpha, \beta}$ (i.e., the fraction of nodes which are active on
+ either of the layers, but not on both) between all pairs of
+ layers. The layers are given as input in the
+ files \textit{layer1}, \textit{layer2}, etc.
+
+ Each input file contains the (undirected) edge list of a layer, and
+ each line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{The program prints on \texttt{stdout} a list of lines, in
+ the format:
+
+ \hspace{0.5cm} \textit{layer1 layer2 hamm}
+
+ \noindent where \textit{layer1} and \textit{layer2} are the IDs of
+ the layers, and \textit{hamm} is the value of the normalised Haming
+ distance $H_{layer1, layer2}$. Layers IDs start from zero, are are
+ associated to the layers in the same order in which the layer files
+ are provided on the command line.}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/structure/activity/layer_activity.tex b/doc/latex/latex/structure/activity/layer_activity.tex
new file mode 100644
index 0000000..34fcdd2
--- /dev/null
+++ b/doc/latex/latex/structure/activity/layer_activity.tex
@@ -0,0 +1,25 @@
+%%%
+%%% Layer activity
+%%%
+
+\myprogram{{layer\_activity.py}}
+ {compute the activity of the layers of a multiplex, i.e. the
+ number of active nodes on each layer.}
+ {$<$layer1$>$ [$<$layer2$>$ ...]}
+
+\mydescription{Compute and print on output the activity of the layers
+ of a multiplex network, where the layers are given as input in the
+ files \textit{layer1}, \textit{layer2}, etc.
+
+ Each file contains the (undirected) edge list of a layer, and each
+ line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{A listof lines, where the n-th line is the value of activity
+ of the n-th layer, starting from \textbf{0}.}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/structure/activity/layer_activity_vectors.tex b/doc/latex/latex/structure/activity/layer_activity_vectors.tex
new file mode 100644
index 0000000..f0c2cd6
--- /dev/null
+++ b/doc/latex/latex/structure/activity/layer_activity_vectors.tex
@@ -0,0 +1,27 @@
+\myprogram{{layer\_activity\_vectors.py}}
+ {compute the activity vectors of all the layers of a multiplex.}
+ {$<$layer1$>$ [$<$layer2$>$ ...]}
+
+\mydescription{Compute and print on output the activity vectors of the
+ layers of a multiplex network, where the layers are given as input
+ in the files \textit{layer1}, \textit{layer2}, etc.
+
+ Each input file contains the (undirected) edge list of a layer, and
+ each line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{The program prints on \texttt{stdout} a list of lines, where
+ the n-th line contains the activity vector of the n-th layer, i.e. a
+ bit-string where each bit is set to ``1'' if the corresponding node
+ is active on the n-th layer, and to ``0'' otherwise.
+
+ \noindent As usual, node IDs start from zero and proceed
+ sequentially, without gaps, i.e., if a node ID is not present in any
+ of the layer files given as input, the program considers it as being
+ isolated on all the layers.}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/structure/activity/multiplexity.tex b/doc/latex/latex/structure/activity/multiplexity.tex
new file mode 100644
index 0000000..b5c5506
--- /dev/null
+++ b/doc/latex/latex/structure/activity/multiplexity.tex
@@ -0,0 +1,30 @@
+\myprogram{{multiplexity.py}}
+ {compute the pairwise multiplexity between all the pairs of
+ layers of a multiplex.}
+ {$<$layer1$>$ $<$layer2$>$ [$<$layer3$>$...]}
+
+\mydescription{Compute and print on output the pairwise multiplexity
+ $Q_{\alpha, \beta}$ (i.e., the fraction of nodes active on both
+ layers) between all pairs of layers. The layers are given as
+ input in the files \textit{layer1}, \textit{layer2}, etc.
+
+ Each input file contains the (undirected) edge list of a layer, and
+ each line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{The program prints on \texttt{stdout} a list of lines, in
+ the format:
+
+ \hspace{0.5cm} \textit{layer1 layer2 mult}
+
+ \noindent where \textit{layer1} and \textit{layer2} are the IDs of
+ the layers, and \textit{mult} is the value of the multiplexity
+ $Q_{layer1, layer2}$. Layers IDs start from zero, are are associated
+ to the layers in the same order in which the layer files are
+ provided on the command line.}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/structure/activity/node_activity.tex b/doc/latex/latex/structure/activity/node_activity.tex
new file mode 100644
index 0000000..882233d
--- /dev/null
+++ b/doc/latex/latex/structure/activity/node_activity.tex
@@ -0,0 +1,25 @@
+%%%
+%%% node_activity
+%%%
+\myprogram{{node\_activity.py}}
+ {compute the activity of the nodes of a multiplex, i.e. the
+ number of layers where each node is not isolated.}
+ {$<$layer1$>$ [$<$layer2$>$ ...]}
+
+\mydescription{Compute and print on output the activity of the nodes
+ of a multiplex network, whose layers are given as input in the files
+ \textit{layer1}, \textit{layer2}, etc.
+
+ Each file contains the (undirected) edge list of a layer, and each
+ line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{A list of lines, where the n-th line is the value of activity
+ of the n-th node, starting from \textbf{0}.}
+
+\myreference{\refcorrelations}
+
diff --git a/doc/latex/latex/structure/activity/node_activity_vectors.tex b/doc/latex/latex/structure/activity/node_activity_vectors.tex
new file mode 100644
index 0000000..ca9301d
--- /dev/null
+++ b/doc/latex/latex/structure/activity/node_activity_vectors.tex
@@ -0,0 +1,28 @@
+\myprogram{{node\_activity\_vectors.py}}
+ {compute the activity vectors of all the nodes of a multiplex.}
+ {$<$layer1$>$ [$<$layer2$>$ ...]}
+
+\mydescription{Compute and print on output the activity vectors of the
+ nodes of a multiplex network, whose layers are given as input in the
+ files \textit{layer1}, \textit{layer2}, etc.
+
+ Each input file contains the (undirected) edge list of a layer, and
+ each line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{The program prints on \texttt{stdout} a list of lines, where
+ the n-th line contains the activity vector of the n-th node, i.e. a
+ bit-string where each bit is set to ``1'' if the node is active on
+ the corresponding layer, and to ``0'' otherwise.
+
+ \noindent As usual, node IDs start from zero and proceed
+ sequentially, without gaps, i.e., if a node ID is not present in any
+ of the layer files given as input, the program considers it as being
+ isolated on all the layers, and will print on output a bit-string of
+ zeros.}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/structure/activity/node_degree_vectors.tex b/doc/latex/latex/structure/activity/node_degree_vectors.tex
new file mode 100644
index 0000000..c86f083
--- /dev/null
+++ b/doc/latex/latex/structure/activity/node_degree_vectors.tex
@@ -0,0 +1,30 @@
+\myprogram{{node\_degree\_vectors.py}}
+ {compute the degree vectors of all the nodes of a multiplex network}
+ {$<$layer1$>$ [$<$layer2$>$ ...]}
+
+\mydescription{Compute and print on output the degree vectors of all
+ the nodes of a multiplex network, whose layers are given as
+ input in the files \textit{layer1}, \textit{layer2}, etc.
+
+ Each file contains the (undirected) edge list of a layer, and each
+ line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{A list of lines, where the n-th line is the
+ vector of degrees of the n-th node, in the format:
+
+ \hspace{0.5cm}\textit{noden\_deg\_lay1 noden\_deg\_lay2 ... noden\_deg\_layM}
+
+ \noindent As usual, node IDs start from zero and proceed
+ sequentially, without gaps, i.e., if a node ID is not present in any
+ of the layer files given as input, the program considers it as being
+ isolated on all the layers.
+
+}
+
+\myreference{\refgrowth\\ \\ \indent \refmetrics}
+
diff --git a/doc/latex/latex/structure/correlations/compute_pearson.tex b/doc/latex/latex/structure/correlations/compute_pearson.tex
new file mode 100644
index 0000000..8202753
--- /dev/null
+++ b/doc/latex/latex/structure/correlations/compute_pearson.tex
@@ -0,0 +1,28 @@
+\myprogram{{compute\_pearson.py}}
+ {compute the Pearson's linear correlation coefficient
+ between two node properties.}
+ {$<$file1$>$ $<$file2$>$}
+
+\mydescription{Compute the Pearson's linear correlation coefficient
+ between two sets of (either integer- or real-valued) node
+ properties provided in the input files \textit{file1}
+ and \textit{file2}. Each input file contains a list of
+ lines, where the n-th line contains the value of a node
+ property for the n-th node. For instance, \textit{file1}
+ and \textit{file2} might contain the degrees of nodes at two
+ distinct layers of a multiplex. However, the program is
+ pretty general and can be used to compute the Pearson's
+ correlation coeffcient between any pairs of node properties.
+ }
+
+\myreturn{The program prints on \texttt{stdout} the value of the
+ Pearson's linear correlation coefficient between the two
+ sets of node properties.
+}
+
+\myreference{\refcorrelations
+
+ \refgrowth
+
+ \refnonlinear
+}
diff --git a/doc/latex/latex/structure/correlations/compute_rho.tex b/doc/latex/latex/structure/correlations/compute_rho.tex
new file mode 100644
index 0000000..957b04c
--- /dev/null
+++ b/doc/latex/latex/structure/correlations/compute_rho.tex
@@ -0,0 +1,32 @@
+\myprogram{{compute\_rho.py}}
+ {compute the Spearman's rank correlation coefficient $\rho$
+ between two rankings.} {$<$file1$>$ $<$file2$>$}
+
+\mydescription{Compute the Spearman's rank correlation coefficient
+ $\rho$ between two rankings provided in the input
+ files \textit{file1} and \textit{file2}. Each input file
+ contains a list of lines, where the n-th line contains the
+ value of rank of the n-th node. For instance, \textit{file1}
+ and \textit{file2} might contain the ranks of nodes induced
+ by the degree sequences of two distinct layers of a
+ multiplex.
+
+ However, the program is pretty general and can be used to
+ compute the Spearman's rank correlation coefficient between
+ any generic pair of rankings.
+
+ N.B.: A C implementation of this program, with the same
+ interface is also available in the executable
+ file \texttt{compute\_rho}.}
+
+
+\myreturn{The program prints on \texttt{stdout} the value of the
+ Spearman's rank correlation coefficient $\rho$ between the
+ two rankings provided as input. }
+
+\myreference{\refcorrelations
+
+ \refgrowth
+
+ \refnonlinear
+ }
diff --git a/doc/latex/latex/structure/correlations/compute_tau.tex b/doc/latex/latex/structure/correlations/compute_tau.tex
new file mode 100644
index 0000000..e6e8589
--- /dev/null
+++ b/doc/latex/latex/structure/correlations/compute_tau.tex
@@ -0,0 +1,31 @@
+\myprogram{{compute\_tau.py}}
+ {compute the Kendall's rank correlation coefficient $\tau_b$
+ between two rankings.} {$<$file1$>$ $<$file2$>$}
+
+\mydescription{Compute the Kendall's rank correlation coefficient
+ $\tau_b$ between two rankings provided in the input
+ files \textit{file1} and \textit{file2}. Each input file
+ contains a list of lines, where the n-th line contains the
+ value of rank of the n-th node. For instance, \textit{file1}
+ and \textit{file2} might contain the ranks of nodes induced
+ by the degree sequences of two distinct layers of a
+ multiplex.
+
+ However, the program is pretty general and can be used to
+ compute the Kendall's rank correlation coefficient between
+ any generic pair of rankings.
+
+ N.B.: This implementation takes properly into account rank
+ ties.}
+
+
+\myreturn{The program prints on \texttt{stdout} the value of the
+ Kendall's rank correlation coefficient $\tau_b$ between the
+ two rankings provided as input. }
+
+\myreference{\refcorrelations
+
+ \refgrowth
+
+ \refnonlinear
+}
diff --git a/doc/latex/latex/structure/correlations/dump_k_q.tex b/doc/latex/latex/structure/correlations/dump_k_q.tex
new file mode 100644
index 0000000..35aef8d
--- /dev/null
+++ b/doc/latex/latex/structure/correlations/dump_k_q.tex
@@ -0,0 +1,42 @@
+M\myprogram{{dump\_k\_q}}
+ {compute the degree sequences of two layers of a multiplex.}
+ {$<$layer1$>$ $<$layer2$>$ $<$pairing$>$}
+
+\mydescription{Compute and dump on \texttt{stdout} the degree
+ sequences of two layers of a multiplex. The input
+ files \textit{layer1} and \textit{layer2} contain the
+ (undirected) edge lists of the two layers, and each line is
+ in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.
+
+ The third file \textit{pairing} is a list of lines in the format:
+
+ \hspace{0.5cm} \textit{IDL1 IDL2}
+
+ where \textit{IDL1} is the ID of a node on layer $1$
+ and \textit{IDL2} is the ID of the same node on layer $2$. For
+ instance, the line:
+
+ \hspace{0.5cm} \textit{5 27}
+
+ indicates that node $5$ on layer $1$ has ID $27$ on layer $2$. }
+
+
+\myreturn{The program prints on \texttt{stdout} the degree of each
+node on the two layers, in the format:
+
+\hspace{0.5cm} \textit{ki qi}
+
+where \textit{ki} is the degree of node \textit{i} on layer $1$
+and \textit{qi} is the degree of node \textit{i} on layer $2$.}
+
+\myreference{\refcorrelations
+
+ \refgrowth
+
+ \refnonlinear
+ }
diff --git a/doc/latex/latex/structure/correlations/fit_knn.tex b/doc/latex/latex/structure/correlations/fit_knn.tex
new file mode 100644
index 0000000..cb90c2b
--- /dev/null
+++ b/doc/latex/latex/structure/correlations/fit_knn.tex
@@ -0,0 +1,50 @@
+\myprogram{{fit\_knn}}
+ {power-law fit of the inter-layer degree correlation
+ function.}
+ {$<$filein$>$ $<$alpha$>$}
+
+\mydescription{Perform a power-law fit of the inter-layer degree
+ correlation function:
+
+ \begin{equation*}
+ \overline{q}(k) = \frac{1}{N_{q}}\sum_{q'} q' P(q'|k)
+ \end{equation*}
+
+ where $k$ is the degree of a node on layer $1$, $q$ is the
+ degree on layer $2$ and $P(q|k)$ is the probability that a
+ node with degree $k$ on layer $1$ has degree $q$ on layer
+ $2$. The program assumes that $\overline{q}(k)$ can be
+ written in the form $a k^{b}$, and computes the two
+ parameters $a$ and $b$ through a linear fit of the log-log
+ plot of $\overline{q}(k)$.
+
+ The input file \textit{filein} contains a list of lines in
+ the format:
+
+ \hspace{0.5cm} \textit{ki qi}
+
+ where \textit{ki} is the degree of node $i$ at layer $1$
+ and \textit{qi} is the degree of node $i$ at layer $2$.
+
+ The second parameter \textit{alpha} is the ratio of the
+ progression used to generate the exponentially-distributed
+ bins for the log-log plot. Typical values of \textit{alpha}
+ are between $1.1$ and $2.0$.
+
+
+ N.B.: The exponent $b$ computed with this method is known to
+ be inaccurate.
+}
+
+
+
+\myreturn{The program prints on \texttt{stdout} the values of the
+ parameters $a$ and $b$ of the power-law fit $\overline{q}(k)
+ = a k^{b}$.}
+
+\myreference{\refcorrelations
+
+ \refgrowth
+
+ \refnonlinear
+ }
diff --git a/doc/latex/latex/structure/correlations/knn_q_from_degrees.tex b/doc/latex/latex/structure/correlations/knn_q_from_degrees.tex
new file mode 100644
index 0000000..cab0905
--- /dev/null
+++ b/doc/latex/latex/structure/correlations/knn_q_from_degrees.tex
@@ -0,0 +1,64 @@
+\myprogram{{knn\_q\_from\_degrees.py}}
+ {compute the inter-layer degree-degree correlation function.}
+ {$<$filein$>$}
+
+\mydescription{Compute the inter-layer degree
+ correlation functions for two layers of a multiplex, using
+ the degrees of the nodes specified in the input file. The
+ format of the input file is as follows
+
+\hspace{0.5cm} \textit{ki qi}
+
+where \textit{ki} and \textit{qi} are, respectively, the degree at
+layer 1 and the degree at layer 2 of node \textit{i}.
+
+ If we consider two layers of a multiplex, and we denote by
+ $k$ the degree of a node on the first layer and by $q$ the
+ degree of the same node on the second layers, the
+ inter-layer degree correlation function is defined as
+
+ \begin{equation*}
+ \overline{k}(q) = \frac{1}{N_{k}}\sum_{k'} k' P(k'|q)
+ \end{equation*}
+
+ where $P(k'|q)$ is the probability that a node with degree
+ $q$ on the second layer has degree equal to $k'$ on the
+ first layer, and $N_k$ is the number of nodes with degree
+ $k$ on the first layer. The quantity $\overline{k}(q)$ is
+ the expected degree at layer $1$ of node that have degree
+ equal to $q$ on layer $2$. The dual quantity:
+
+ \begin{equation*}
+ \overline{q}(k) = \frac{1}{N_{q}}\sum_{q'} q' P(q'|k)
+ \end{equation*}
+
+ is the average degree on layer $2$ of nodes having degree
+ $k$ on layer $1$.
+}
+
+
+\myreturn{The program prints on \texttt{stdout} a list of lines in
+ the format:
+
+ \hspace{0.5cm} \textit{k $\overline{q}(k)$}
+
+ where \textit{k} is the degree on layer $1$ and
+ $\overline{q}(k)$ is the average degree on layer $2$ of
+ nodes having degree equal to $k$ on layer $1$.
+
+ The program also prints on \texttt{stderr} a list of lines in
+ the format:
+
+ \hspace{0.5cm} \textit{q $\overline{k}(q)$}
+
+ where \textit{q} is the degree on layer $2$ and
+ $\overline{k}(q)$ is the average degree on layer $1$ of
+ nodes having degree equal to $q$ on layer $2$.
+ }
+
+\myreference{\refcorrelations
+
+ \refgrowth
+
+ \refnonlinear
+ }
diff --git a/doc/latex/latex/structure/correlations/knn_q_from_layers.tex b/doc/latex/latex/structure/correlations/knn_q_from_layers.tex
new file mode 100644
index 0000000..f124e55
--- /dev/null
+++ b/doc/latex/latex/structure/correlations/knn_q_from_layers.tex
@@ -0,0 +1,80 @@
+\myprogram{{knn\_q\_from\_layers.py}}
+ {compute intra-layer and inter-layer degree-degree
+ correlation coefficients.} {$<$layer1$>$ $<$layer2$>$}
+
+\mydescription{Compute the intra-layer and the inter-layer degree
+ correlation functions for two layers given as input. The
+ intra-layer degree correlation function quantifies the
+ presence of degree-degree correlations in a single layer
+ network, and is defined as:
+
+ \begin{equation*}
+ \avg{k_{nn}(k)} = \frac{1}{k N_k}\sum_{k'}k'P(k'|k)
+ \end{equation*}
+
+ where $P(k'|k)$ is the probability that a neighbour of a
+ node with degree $k$ has degree $k'$, and $N_k$ is the
+ number of nodes with degree $k$. The quantity
+ $\avg{k_{nn}(k)}$ is the average degree of the neighbours of
+ nodes having degree equal to $k$.
+
+ If we consider two layers of a multiplex, and we denote by
+ $k$ the degree of a node on the first layer and by $q$ the
+ degree of the same node on the second layers, the
+ inter-layer degree correlation function is defined as
+
+ \begin{equation*}
+ \overline{k}(q) = \sum_{k'} k' P(k'|q)
+ \end{equation*}
+
+ where $P(k'|q)$ is the probability that a node with degree
+ $q$ on the second layer has degree equal to $k'$ on the
+ first layer, and $N_q$ is the number of nodes with degree
+ $q$ on the second layer. The quantity $\overline{k}(q)$ is
+ the expected degree at layer $1$ of node that have degree
+ equal to $q$ on layer $2$. The dual quantity:
+
+ \begin{equation*}
+ \overline{q}(k) = \sum_{q'} q' P(q'|k)
+ \end{equation*}
+
+ is the average degree on layer $2$ of nodes having degree
+ $k$ on layer $1$.
+}
+
+
+\myreturn{The program creates two output files, respectively called
+
+\hspace{0.5cm} \textit{file1\_file2\_k1}
+
+and
+
+\hspace{0.5cm} \textit{file1\_file2\_k2}
+
+The first file contains a list of lines in the format:
+
+\hspace{0.5cm} \textit{k $\avg{k_{nn}(k)}$ $\sigma_k$
+$\overline{q}(k)$ $\sigma_{\overline{q}}$}
+
+where $k$ is the degree at first layer, $\avg{k_{nn}(k)}$ is the
+average degree of the neighbours at layer $1$ of nodes having degree
+$k$ at layer $1$, $\sigma_k$ is the standard deviation associated to
+$\avg{k_{nn}(k)}$, $\overline{q}(k)$ is the average degree at layer
+$2$ of nodes having degree equal to $k$ at layer $1$, and
+$\sigma_{\overline{q}}$ is the standard deviation associated to
+$\overline{q}(k)$.
+
+The second file contains a similar list of lines, in the format:
+
+\hspace{0.5cm} \textit{q $\avg{q_{nn}(q)}$ $\sigma_q$
+$\overline{k}(q)$ $\sigma_{\overline{k}}$}
+
+with obvious meaning.
+}
+
+\myreference{\refcorrelations
+
+ \refgrowth
+
+ \refnonlinear
+ }
diff --git a/doc/latex/latex/structure/correlations/rank_nodes.tex b/doc/latex/latex/structure/correlations/rank_nodes.tex
new file mode 100644
index 0000000..b1a970a
--- /dev/null
+++ b/doc/latex/latex/structure/correlations/rank_nodes.tex
@@ -0,0 +1,19 @@
+\myprogram{{rank\_nodes.py}}
+ {rank the nodes of a layer according to a given structural
+ descriptor.} {$<$prop\_file$>$}
+
+\mydescription{Get a file as input, whose n-th line corresponds to the value of a
+ certain property of the n-th node, and rank the nodes according to
+ that property, taking into account ranking ties properly.
+
+ For example, if \textit{propfile} contains the degrees of the nodes
+ at a certain layer of the multiplex, the computes the ranking induced
+ by degrees, where the node with the highest degree will be assigned a
+ rank equal to \textbf{1} (one).
+}
+
+\myreturn{The program prints on \texttt{stdout} a list of lines, where
+ the n-th line contains the rank of the n-th node corresponding to the
+ values of the structural descriptor provided in the input file.}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/structure/correlations/rank_nodes_thresh.tex b/doc/latex/latex/structure/correlations/rank_nodes_thresh.tex
new file mode 100644
index 0000000..3b430d1
--- /dev/null
+++ b/doc/latex/latex/structure/correlations/rank_nodes_thresh.tex
@@ -0,0 +1,18 @@
+\myprogram{{rank\_nodes\_thresh.py}}
+ {rank the nodes of a layer whose value of a given structural
+ descriptor is above a threshold.} {$<$prop\_file$>$ $<$thresh$>$}
+
+\mydescription{Get a file as input, whose n-th line corresponds to the value of a
+ certain property of the n-th node, and rank the nodes according to
+ that property, taking into account ranking ties properly. The rank of
+ all the nodes whose value of the structural descriptor is smaller
+ than the threshold \textit{thresh} specified as second parameter is
+ set to \textbf{0} (ZERO). }
+
+\myreturn{The program prints on \texttt{stdout} a list of lines, where
+ the n-th line contains the rank of the n-th node corresponding to the
+ values of the structural descriptor provided in the input file, or
+ zero if such desxriptor is below the specified
+ threshold \textit{thresh}.}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/structure/correlations/rank_occurrence.tex b/doc/latex/latex/structure/correlations/rank_occurrence.tex
new file mode 100644
index 0000000..96fb914
--- /dev/null
+++ b/doc/latex/latex/structure/correlations/rank_occurrence.tex
@@ -0,0 +1,24 @@
+\myprogram{{rank\_occurrence.py}}
+ {compute the intersection of two rankings.}
+ {$<$rank1$>$ $<$rank2$>$ $<$increment$>$}
+
+\mydescription{Get two rankings \textit{rank1} and \textit{rank2}
+ and compute the size of
+the \textit{k}-intersection, i.e. the number of elements which are
+present in the first k positions of both rankings, as a function
+of \textit{k}. The parameter \textit{increment} determines the
+distance between two subsequent values of \textit{k}.
+
+Each input file is a list of node IDs, one per line, where the first
+line contains the ID of the highest ranked node.
+}
+
+\myreturn{The program prints on \texttt{stdout} a list of lines in the
+format:
+
+ \hspace{0.5cm} \textit{k num\_k}
+
+ where \textit{num\_k} is the number of nodes which are present in
+ the first \textit{k} positions of both rankings.}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/structure/metrics/aggregate_layers_w.tex b/doc/latex/latex/structure/metrics/aggregate_layers_w.tex
new file mode 100644
index 0000000..8917e3e
--- /dev/null
+++ b/doc/latex/latex/structure/metrics/aggregate_layers_w.tex
@@ -0,0 +1,30 @@
+\myprogram{{aggregate\_layers\_w.py}}
+ {compute the (weighted) aggregated graph associated to a
+ multiplex.} {$<$layer1$>$ $<$layer2$>$ [$<$layer3$>$...]}
+
+\mydescription{Compute and print on output the edge list of the
+ weighted aggregated graph associated to the multiplex
+ network given on input. An edge is present in the
+ aggregated graph if it exists in at least one of the M
+ layers of the multiplex.
+
+ Each input file contains the (undirected) edge list of a layer, and
+ each line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{The program prints on \texttt{stdout} the edge list of the
+ aggregated graph associated to the multiplex network. The edge list
+ is a list of lines in the format:
+
+
+ \hspace{0.5cm} \textit{ID1 ID2 weight}
+
+ \noindent where \textit{ID1} and \textit{ID2} are the IDs of the two
+ nodes and \textit{weight} is the number of layers in which an edge
+ between \textit{ID1} and \textit{ID2} exists.}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/structure/metrics/avg_edge_overlap.tex b/doc/latex/latex/structure/metrics/avg_edge_overlap.tex
new file mode 100644
index 0000000..4df2d51
--- /dev/null
+++ b/doc/latex/latex/structure/metrics/avg_edge_overlap.tex
@@ -0,0 +1,42 @@
+\myprogram{{avg\_edge\_overlap.py}}
+ {compute the average edge overlap of a multiplex.}
+ {$<$layer1$>$ [$<$layer2$>$...]}
+
+\mydescription{Compute and print on output the average edge overlap
+
+ \begin{equation*} \omega^{*}
+ = \frac{\sum_{i}\sum_{j>i}\sum_{\alpha}a_{ij}\lay{\alpha}}{ \sum_{i}\sum_{j>i}(1
+ - \delta_{0,\sum_{\alpha}a_{ij}\lay{\alpha}})} \end{equation*}
+
+ \noindent i.e., the expected \textit{number} of layers on which an
+ edge of the multiplex exists, and the corresponding normalised
+ quantity:
+
+ \begin{equation*}
+ \omega = \frac{\sum_{i}\sum_{j>i}\sum_{\alpha}a_{ij}\lay{\alpha}}{M \sum_{i}\sum_{j>i}(1
+ - \delta_{0,\sum_{\alpha}a_{ij}\lay{\alpha}})}
+ \end{equation*}
+
+ \noindent that is the expected \textit{fraction} of layers on which
+ an edge of the multiplex is present.
+
+ Each input file contains the (undirected) edge list of a layer, and
+ each line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{The program prints on \texttt{stdout} a single line, in the
+ format:
+
+ \hspace{0.5cm} \textit{omega\_star omega}
+
+ \noindent where \textit{omega\_star} and \textit{omega} are,
+ respectively, the expected number and fraction of layers in which an
+ edge is present.}
+
+\myreference{\refmetrics
+
+ \vspace{0.5cm}\refvisibility}
diff --git a/doc/latex/latex/structure/metrics/cartography_from_columns.tex b/doc/latex/latex/structure/metrics/cartography_from_columns.tex
new file mode 100644
index 0000000..8e797af
--- /dev/null
+++ b/doc/latex/latex/structure/metrics/cartography_from_columns.tex
@@ -0,0 +1,35 @@
+\myprogram{{cartography\_from\_columns.py}}
+ {compute total and participation coefficient of generic
+ structural descriptors of the nodes of a multiplex.}
+ {$<$filein$>$ $<$col1$>$ $<$col2$>$ [$<$col3$>$...]}
+
+\mydescription{Compute and print on output the sum and the
+ corresponding participation coefficient of a generic
+ structural descriptor of the nodes of a multiplex.
+
+ \noindent The input file is a generic collection of
+ single-space-separated columns, where each line corresponds to a
+ node. The user must specify the IDs of the columns which contain
+ the node structural descriptors to be used in the cartography
+ diagram. Columns IDs start from ZERO. For example:
+
+ \textbf{python cartography\_from\_layers.py filein.txt 0
+ 2 4 6 8}
+
+ \noindent will create a cartography diagram assuming that the
+ multiplex network has five layers, and that the node structural
+ descriptors at each layers are contained in the first (0), third
+ (2), fifth (4), seventh (6) and nineth (8) columns of each row.}
+
+
+\myreturn{The program prints on \texttt{stdout} a list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{tot\_n P\_n}
+
+ where \textit{tot\_n} is the sum over the layers of the considered
+ structural descriptor for node $n$, and \textit{P\_n} is the
+ associated participation coefficient
+ }
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/structure/metrics/cartography_from_deg_vectors.tex b/doc/latex/latex/structure/metrics/cartography_from_deg_vectors.tex
new file mode 100644
index 0000000..848ffd1
--- /dev/null
+++ b/doc/latex/latex/structure/metrics/cartography_from_deg_vectors.tex
@@ -0,0 +1,32 @@
+\myprogram{{cartography\_from\_deg\_vectors.py}}
+ {create a multiplex cartography diagram.}
+ {$<$node\_deg\_vectors$>$}
+
+\mydescription{Compute and print on output the total degree and the
+ multiplex participation coefficient of all the nodes of a
+ multiplex network whose list of node degree vectors is
+ provided as input. The input file is in the format:
+
+ \hspace{0.5cm} \textit{IDn\_deg1 IDn\_deg\_2 ... IDn\_degM}
+
+ \noindent where \textit{IDn\_degX} is the degree of node $n$ at
+ layer $X$. The input file can be generated using the
+ script \texttt{node\_degree\_vectors.py}.}
+
+
+\myreturn{The program prints on \texttt{stdout} a list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{tot\_deg part\_coeff}
+
+ \noindent where \textit{tot\_deg} is the total degree of the node
+ and \textit{part\_coeff} is the corresponding participation
+ coefficient.
+
+ \noindent As usual, node IDs start from zero and proceed
+ sequentially, without gaps, so if one of the lines in the input
+ files contains just zeros, the program considers the corresponding
+ node as being isolated on all the layers, and both its total degree
+ and multiplex participation coefficient are set equal to zero. }
+
+\myreference{\refmetrics}
diff --git a/doc/latex/latex/structure/metrics/cartography_from_layers.tex b/doc/latex/latex/structure/metrics/cartography_from_layers.tex
new file mode 100644
index 0000000..8958cef
--- /dev/null
+++ b/doc/latex/latex/structure/metrics/cartography_from_layers.tex
@@ -0,0 +1,45 @@
+\myprogram{{cartography\_from\_layers.py}}
+ {compute the total degree and the multiplex participation
+ coefficient of all the nodes of a multiplex.} {$<$layer1$>$
+ $<$layer2$>$ [$<$layer3$>$...]}
+
+\mydescription{Compute and print on output the total degree and the multiplex participation
+ coefficient $P_i$ for each node $i$ of a multiplex. The
+ participation coefficient is defined as:
+
+ \begin{equation*}
+ P_i=\frac{M}{M-1}\left[1-\sum_{\alpha=1}^M\biggl(\frac{k_i^{[\alpha]}}{o_i}\biggr)^2\right]
+ \end{equation*}
+
+ \noindent Note that $P_i$ takes values in $[0,1]$, where $P_i=0$
+ if and only if node $i$ is active on exactly one of the layers,
+ while $P_i=1$ if node $i$ has equal degree on all the $M$ layers.
+
+ Each input file contains the (undirected) edge list of a layer, and
+ each line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{The program prints on \texttt{stdout} a list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{deg\_n P\_n col\_n}
+
+ where \textit{deg\_n} is the total degree of node $n$, \textit{P\_n}
+ is the participation coefficient of node $n$ and \textit{col} is the
+ integer representation of the activity bitstring of node $n$, which
+ is a number between $0$ and $2^{M}-1$. The field \textit{col} might
+ be useful for the visualisation of the multiplex cartography
+ diagram, where it would be possible to associate different colors to
+ nodes having different node activity patterns.
+
+ \noindent As usual, node IDs start from zero and proceed
+ sequentially, without gaps, i.e., if a node ID is not present in any
+ of the layer files given as input, the program considers it as being
+ isolated on all the layers, and is set to zero.
+ }
+
+\myreference{\refmetrics}
diff --git a/doc/latex/latex/structure/metrics/edge_overlap.tex b/doc/latex/latex/structure/metrics/edge_overlap.tex
new file mode 100644
index 0000000..64d7dbf
--- /dev/null
+++ b/doc/latex/latex/structure/metrics/edge_overlap.tex
@@ -0,0 +1,36 @@
+\myprogram{{edge\_overlap.py}}
+ {compute the edge overlap of all the edges of the
+ multiplex.}
+ {$<$layer1$>$ [$<$layer2$>$...]}
+
+\mydescription{Compute and print on output the edge overlap $o_{ij}$ of each
+ edge of the multiplex. Given a pair of nodes $(i,j)$ that
+ are directly connected on at least one of the $M$ layers,
+ the edge overlap $o_{ij}$ is defined as:
+
+ \begin{equation*}
+ o_{ij} = \sum_{\alpha}a_{ij}\lay{\alpha}
+ \end{equation*}
+
+ \noindent i.e., the number of layers on which the edge $(i,j)$
+ exists.
+
+
+ Each input file contains the (undirected) edge list of a layer, and
+ each line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{The program prints on \texttt{stdout} a list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{ID\_1 ID\_2 overlap}
+
+ \noindent where \textit{ID\_1} and \textit{ID\_2} are the IDs of the
+ end-points of the edge, and \textit{overlap} is the number of layers
+ in which the edge exists.}
+
+\myreference{\refmetrics}
diff --git a/doc/latex/latex/structure/metrics/intersect_layers.tex b/doc/latex/latex/structure/metrics/intersect_layers.tex
new file mode 100644
index 0000000..0824400
--- /dev/null
+++ b/doc/latex/latex/structure/metrics/intersect_layers.tex
@@ -0,0 +1,28 @@
+\myprogram{{intersect\_layers.py}}
+ {compute the intersection graph associated to a
+ multiplex.} {$<$layer1$>$ $<$layer2$>$ [$<$layer3$>$...]}
+
+\mydescription{Compute and print on output the edge list of the
+ intersection graph associated to the multiplex network
+ given on input, where an edge exists only if it is
+ present on \textbf{all} the layers of the multiplex.
+
+ Each input file contains the (undirected) edge list of a layer, and
+ each line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{The program prints on \texttt{stdout} the edge list of the
+ intersection graph associated to the multiplex network. The edge
+ list is a list of lines in the format:
+
+
+ \hspace{0.5cm} \textit{ID1 ID2}
+
+ \noindent where \textit{ID1} and \textit{ID2} are the IDs of the two
+ nodes.}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/structure/metrics/overlap_degree.tex b/doc/latex/latex/structure/metrics/overlap_degree.tex
new file mode 100644
index 0000000..500a76a
--- /dev/null
+++ b/doc/latex/latex/structure/metrics/overlap_degree.tex
@@ -0,0 +1,45 @@
+\myprogram{{overlap\_degree.py}}
+ {compute the total (overlapping) degree of all the nodes of
+ a multiplex and the corresponding Z-score. } {$<$layer1$>$ $<$layer2$>$ [$<$layer3$>$...]}
+
+\mydescription{Compute and print on output the total degree $o_i$ of each
+ node $i$ of a multiplex, defined as:
+
+ \begin{equation*}
+ o_{i} = \sum_{\alpha}\sum_{j}a_{ij}\lay{\alpha}
+ \end{equation*}
+
+ \noindent and the corresponding Z-score:
+
+ \begin{equation*}
+ z(o_i) = \frac{o_i - \avg{o}}{\sigma_o}
+ \end{equation*}
+
+ \noindent where $\avg{o}$ and $\sigma_o$ are, respectively, the mean
+ and the standard deviation of the total degree computed over all the
+ active nodes of the multiplex.
+
+
+ Each input file contains the (undirected) edge list of a layer, and
+ each line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{The program prints on \texttt{stdout} a list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{ID\_n deg\_n z\_n}
+
+ where \textit{ID\_n} is the ID of the node, \textit{deg\_n} is its
+ total degree, and \textit{z\_n} is the corresponding Z-score.
+
+ \noindent As usual, node IDs start from zero and proceed
+ sequentially, without gaps, i.e., if a node ID is not present in any
+ of the layer files given as input, the program considers it as being
+ isolated on all the layers, and the node is omitted from the
+ output.}
+
+\myreference{\refmetrics}
diff --git a/doc/latex/latex/structure/metrics/part_coeff.tex b/doc/latex/latex/structure/metrics/part_coeff.tex
new file mode 100644
index 0000000..f3afd7d
--- /dev/null
+++ b/doc/latex/latex/structure/metrics/part_coeff.tex
@@ -0,0 +1,43 @@
+\myprogram{{part\_coeff.py}}
+ {compute the multiplex partifipation coefficient of all the nodes of
+ a multiplex.} {$<$layer1$>$ $<$layer2$>$ [$<$layer3$>$...]}
+
+\mydescription{Compute and print on output the multiplex participation
+ coefficient $P_i$ for each node $i$ of a multiplex. The
+ participation coefficient is defined as:
+
+ \begin{equation*}
+ P_i=\frac{M}{M-1}\left[1-\sum_{\alpha=1}^M\biggl(\frac{k_i^{[\alpha]}}{o_i}\biggr)^2\right]
+ \end{equation*}
+
+ \noindent Note that $P_i$ takes values in $[0,1]$, where $P_i=0$
+ if and only if node $i$ is active on exactly one of the layers,
+ while $P_i=1$ if node $i$ has equal degree on all the $M$ layers.
+
+ Each input file contains the (undirected) edge list of a layer, and
+ each line is in the format:
+
+ \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID}
+
+ where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two
+ endpoints of an edge.}
+
+\myreturn{The program prints on \texttt{stdout} a list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{deg\_n P\_n col\_n}
+
+ where \textit{deg\_n} is the total degree of node $n$, \textit{P\_n}
+ is the participation coefficient of node $n$ and \textit{col} is the
+ integer representation of the activity bitstring of node $n$, which
+ is a number between $0$ and $2^{M}-1$. The field \textit{col} might
+ be useful in visualisations, where it would be possible to associate
+ different colors to nodes having diffrent node activity patterns.
+
+ \noindent As usual, node IDs start from zero and proceed
+ sequentially, without gaps, i.e., if a node ID is not present in any
+ of the layer files given as input, the program considers it as being
+ isolated on all the layers, and is set to zero.
+ }
+
+\myreference{\refmetrics}
diff --git a/doc/latex/latex/structure/reinforcement/reinforcement.tex b/doc/latex/latex/structure/reinforcement/reinforcement.tex
new file mode 100644
index 0000000..a65b05e
--- /dev/null
+++ b/doc/latex/latex/structure/reinforcement/reinforcement.tex
@@ -0,0 +1,21 @@
+%%%
+%%% Layer activity
+%%%
+
+\myprogram{{reinforcement.py}}
+ {compute the probability to have a link between two nodes in layer $1$ given their weight in layer $2$.}
+ {$<$layer1$>$ $<$layer2$>$ $<N_{bins}>$ $<min_{value}>$ $<max_{value}>$}
+
+\mydescription{Compute and print on output the probability to have a link between two nodes in layer $1$ given their weight in layer $2$.
+As input are given the files \textit{layer1}, \textit{layer2}, the number of bins for the link weights of the second layer, the minimum and the maximum values of the binning.
+
+ The first file contains the binary edge list of layer $1$, the second file contains the weighted edge list of layer $2$. each
+ line is in the format:
+
+ \hspace{0.5cm}\textit{bin\_min} \textit{bin\_max} \textit{freq}
+
+ where \textit{bin\_min} and \textit{bin\_max} are the minimum and maximum values of the link weights of layer $2$ in that binning, and \textit{freq} is the probability to have a link on layer $1$ given such weight in layer $2$.}
+
+\myreturn{A list of lines, where the n-th line is the minimum and maximum values of the weight of the links in layer $2$ in the n-th bin, and the frequency to have a link on layer $2$ given that weight.}
+
+\myreference{\refmetrics}
diff --git a/doc/latex/mammult_doc.tex b/doc/latex/mammult_doc.tex
new file mode 100644
index 0000000..4d93d88
--- /dev/null
+++ b/doc/latex/mammult_doc.tex
@@ -0,0 +1,265 @@
+\documentclass[a4paper,11pt]{book}
+
+\usepackage[british]{babel}
+\usepackage[latin1]{inputenc}
+\usepackage{hyperref}
+\usepackage{amsmath, amssymb}
+
+\newcommand{\lay}[1]{^{[#1]}}
+\newcommand{\avg}[1]{\langle #1 \rangle}
+
+
+\newcommand{\myprogram}[3]{\subsubsection{\texttt{#1}}
+ \textbf{NAME}
+
+ {\textbf{#1} - #2}
+
+ \vspace{0.5cm}
+ \noindent
+ \textbf{SYNOPSYS}
+
+ {\textbf{#1} { }\texttt{\textit{#3} } }
+}
+
+\newcommand{\mydescription}[1]{
+ \vspace{0.5cm}
+ \noindent
+ \textbf{DESCRIPTION}
+
+ {#1}
+}
+
+\newcommand{\myreturn}[1]{
+ \vspace{0.5cm}
+ \noindent
+ \textbf{OUTPUT}
+
+ {#1}
+}
+
+
+\newcommand{\myreference}[1]{
+ \vspace{0.5cm}
+ \noindent
+ \textbf{REFERENCE}
+
+ {#1}
+}
+
+%%
+%% REFERENCES
+%%
+
+\newcommand{\refgrowth}{V. Nicosia, G. Bianconi, V. Latora,
+ M. Barthelemy, ``Growing multiplex networks'',
+ \textit{Phys. Rev. Lett.} {\bf 111}, 058701 (2013).
+
+ Link to paper: \url{http://prl.aps.org/abstract/PRL/v111/i5/e058701}
+}
+\newcommand{\refnonlinear}{V. Nicosia, G. Bianconi, V. Latora,
+ M. Barthelemy, ``Non-linear growth and condensation in multiplex
+ networks'', \textit{Phys. Rev. E} {\bf 90}, 042807 (2014).
+
+ Link to paper: \url{http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807}
+}
+\newcommand{\refmetrics}{F. Battiston, V. Nicosia, V. Latora,
+ ``Structural measures for multiplex networks'',
+ \textit{Phys. Rev. E} {\bf 89}, 032804 (2014).
+
+ Link to paper: \url{http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032804}
+}
+\newcommand{\refcorrelations}{V. Nicosia, V. Latora, ``Measuring and
+ modeling correlations in multiplex networks'', \textit{Phys. Rev. E}
+ {\bf 92}, 032805 (2015).
+
+ Link to paper: \url{http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805}}
+
+\newcommand{\refreducibility}{M. De Domenico, V. Nicosia, A. Arenas,
+ V. Latora, \textit{``Structural reducibility of multilayer
+ networks''}, Nat. Commun. {\bf 6}, 6864 (2015).
+
+ Link to paper: \url{http://www.nature.com/ncomms/2015/150423/ncomms7864/full/ncomms7864.html}
+}
+\newcommand{\refvisibility}{L. Lacasa, V. Nicosia, V. Latora,
+ \textit{``Network structure of multivariate time series''}, accepted
+ for publication in Scientific Reports, arxiv:1408.0925 (2015).
+
+ Link to paper: \url{http://arxiv.org/abs/1408.0925}
+}
+
+\newcommand{\refbiased}{F. Battiston, V. Nicosia, V. Latora,
+ \textit{``Biased random walks on multiplex networks''}, arxiv:1505.01378 (2015).
+
+ Link to paper: \url{http://arxiv.org/abs/1505.01378}
+}
+\newcommand{\refising}{F. Battiston, A. Cairoli, V. Nicosia, A. Baule, V. Latora,
+ \textit{``Interplay between consensus and coherence in a model of interacting opinions''}, accepted
+ for publication in Physica D, arxiv:1506.04544 (2015).
+
+ Link to paper: \url{http://arxiv.org/abs/1506.04544}
+}
+\newcommand{\refcommunity}{F. Battiston, J. Iacovacci, V. Nicosia, G. Bianconi, V. Latora,
+ \textit{``Emergence of multiplex communities in collaboration networks''}, arxiv:1506.01280 (2015).
+
+ Link to paper: \url{http://arxiv.org/abs/1506.01280}
+}
+
+\newcommand{\refaxelrod}{F. Battiston, V. Nicosia, V. Latora, M. San Miguel,
+ \textit{``Layered social influence promotes multiculturality''}, in preparation (2015).
+
+ %Link to paper: \url{http://arxiv.org/abs/inpreparation}
+}
+\newcommand{\refmotifs}{F. Battiston, M. Chavez, V. Nicosia, V. Latora,
+ \textit{``Multilayer motifs in brain networks''}, in preparation (2015).
+
+ %Link to paper: \url{http://arxiv.org/abs/inpreparation}
+}
+
+\title{MAMMULT: Metrics And Models for MULTilayer networks}
+
+
+\begin{document}
+
+\maketitle
+
+\chapter{Structural descriptors}
+
+\section{Basic node, edge, and layer properties}
+
+\subsection{Node and layer activity}
+
+This section includes programs related to the computation of node and
+layer activity, activity vectors, pairwise multiplexity, pairwise
+normalised Hamming distance, node degree vectors.
+
+\input{./latex/structure/activity/node_activity.tex}
+\input{./latex/structure/activity/layer_activity.tex}
+\input{./latex/structure/activity/node_activity_vectors.tex}
+\input{./latex/structure/activity/layer_activity_vectors.tex}
+\input{./latex/structure/activity/multiplexity.tex}
+\input{./latex/structure/activity/hamming_dist.tex}
+\input{./latex/structure/activity/node_degree_vectors.tex}
+\input{./latex/structure/activity/degs_to_binary.tex}
+\input{./latex/structure/activity/degs_to_activity_overlap.tex}
+
+\subsection{Layer aggregation}
+
+This section includes programs to obtain various single-layer
+aggregated graphs associated to a multiplex network.
+
+\input{./latex/structure/metrics/aggregate_layers_w.tex}
+\input{./latex/structure/metrics/intersect_layers.tex}
+
+\subsection{Node degree, participation coefficient, cartography}
+
+This section includes programs to compute the total degree and
+participation coefficient of each node, and to draw the cartography
+diagram of a multiplex.
+
+\input{./latex/structure/metrics/overlap_degree.tex}
+\input{./latex/structure/metrics/cartography_from_layers.tex}
+\input{./latex/structure/metrics/cartography_from_deg_vectors.tex}
+\input{./latex/structure/metrics/cartography_from_columns.tex}
+
+\subsection{Edge overlap, reinforcement}
+This section includes programs to compute the egde overlap and to
+evaulate the edge reinforcement effect.
+
+\input{./latex/structure/metrics/edge_overlap.tex}
+\input{./latex/structure/metrics/avg_edge_overlap.tex}
+\input{./latex/structure/reinforcement/reinforcement.tex}
+
+\section{Inter-layer degree correlations}
+
+\subsection{Node ranking}
+
+This section includes various utilities to compute and compare node
+rankings induced by any generic structural node property, including
+degree at different layers.
+
+\input{./latex/structure/correlations/rank_nodes.tex}
+\input{./latex/structure/correlations/rank_nodes_thresh.tex}
+\input{./latex/structure/correlations/rank_occurrence.tex}
+
+\subsection{Interlayer degree correlation coefficients}
+
+This section includes programs for the computation of various
+inter-layer degree correlation coefficients.
+
+\input{./latex/structure/correlations/compute_pearson.tex}
+\input{./latex/structure/correlations/compute_rho.tex}
+\input{./latex/structure/correlations/compute_tau.tex}
+
+
+\subsection{Interlayer degree correlation functions}
+
+This section includes programs to compute intra-layer and inter-layer
+degree correlation functions, and to fit those functions with a
+power-law.
+
+
+\input{./latex/structure/correlations/dump_k_q.tex}
+\input{./latex/structure/correlations/knn_q_from_layers.tex}
+%% \input{./latex/structure/correlations/knn_q_from_layers_log.tex}
+\input{./latex/structure/correlations/knn_q_from_degrees.tex}
+%% \input{./latex/structure/correlations/knn_q_from_degrees_log.tex}
+\input{./latex/structure/correlations/fit_knn.tex}
+
+\chapter{Models of multi-layer networks}
+
+\section{Null models}
+
+\subsection{Null-models of node and layer activity}
+
+\input{./latex/models/nullmodels/model_hypergeometric.tex}
+\input{./latex/models/nullmodels/model_MDM.tex}
+\input{./latex/models/nullmodels/model_MSM.tex}
+\input{./latex/models/nullmodels/model_layer_growth.tex}
+
+
+\section{Growing multiplex networks}
+
+\subsection{Linear preferential attachment}
+
+\input{./latex/models/growth/nibilab_linear_delta.tex}
+\input{./latex/models/growth/nibilab_linear_delay.tex}
+\input{./latex/models/growth/nibilab_linear_delay_mix.tex}
+\input{./latex/models/growth/nibilab_linear_random_times.tex}
+%%\input{./latex/models/growth/nibilab_semilinear.tex}
+
+\subsection{Non-linear preferential attachment}
+
+\input{./latex/models/growth/nibilab_nonlinear.tex}
+
+
+\subsection{Utilities}
+
+\input{./latex/models/growth/node_deg_over_time.tex}
+
+\section{Multiplex networks with inter-layer degree correlations}
+
+\subsection{Models based on simulated annealing}
+
+\input{./latex/models/correlations/tune_rho.tex}
+\input{./latex/models/correlations/tune_qnn_adaptive.tex}
+
+
+\chapter{Dynamics on multi-layer networks}
+
+\section{Interacting opinions - Multilayer ising model}
+
+\input{./latex/dynamics/Ising/multiplex_ising.tex}
+
+\section{Biased random walks}
+
+\subsection{Stationary distribution}
+
+\input{./latex/dynamics/randomwalks/statdistr2.tex}
+
+\subsection{Entropy rate}
+
+\input{./latex/dynamics/randomwalks/entropyrate2add.tex}
+\input{./latex/dynamics/randomwalks/entropyrate2mult.tex}
+\input{./latex/dynamics/randomwalks/entropyrate2int.tex}
+
+\end{document}
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