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<a href="#NAME">NAME</a>
<a href="#SYNOPSIS">SYNOPSIS</a>
<a href="#DESCRIPTION">DESCRIPTION</a>
<a href="#PARAMETERS">PARAMETERS</a>
<a href="#EXAMPLES">EXAMPLES</a>
<a href="#SEE-ALSO">SEE ALSO</a>
<a href="#REFERENCES">REFERENCES</a>
<a href="#AUTHORS">AUTHORS</a>
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<ol class='man-decor man-head man head'>
<li class='tl'>ws(1)</li>
<li class='tc'>www.complex-networks.net</li>
<li class='tr'>ws(1)</li>
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<h2 id="NAME">NAME</h2>
<p class="man-name">
<code>ws</code> - <span class="man-whatis">Create a small-world graph using the Watts-Strogatz model</span>
</p>
<h2 id="SYNOPSIS">SYNOPSIS</h2>
<p><code>ws</code> <var>N</var> <var>m</var> <em>p</em> [SHOW]</p>
<h2 id="DESCRIPTION">DESCRIPTION</h2>
<p><code>ws</code> creates a small-world undirected graph with 'N' nodes using the
Watts-Strogatz small-world network model. The nodes are initially
placed around a circle and each node is connected to its 'm' closest
neighbours on either side. Then, each edge is rewired (independently)
with probability 'p'. The program prints on output the edge-list of
the resulting graph.</p>
<h2 id="PARAMETERS">PARAMETERS</h2>
<dl>
<dt class="flush"><var>N</var></dt><dd><p> Number of nodes in the final graph.</p></dd>
<dt class="flush"><var>m</var></dt><dd><p> Number of neighbours on the circle graph to which a node is
connected on either side (i.e., each node will initially have
'2m' edges).</p></dd>
<dt class="flush"><em>p</em></dt><dd><p> Edge rewiring probability.</p></dd>
<dt class="flush">SHOW</dt><dd><p> If the fourth (optional) parameter is equal to <code>SHOW</code>, the program
will print on STDERR the number of edges rewired while constructing
the graph.</p></dd>
</dl>
<h2 id="EXAMPLES">EXAMPLES</h2>
<p>The command:</p>
<pre><code> $ ws 100 3 0.1
0 95
0 2
0 3
1 2
1 24
1 4
2 3
....
99 0
99 56
99 2
$
</code></pre>
<p>creates a Watts-Strogatz small-world network with 'N=100' nodes and
'K=m*N=300' edges, where each edge is independently rewired with
probability 'p=0.1'. The output of <code>ws</code> is the edge-list of the
resulting graph. Notice that in this case the first edge od node <code>0</code>
has been rewired and connected to node <code>95</code>. In order to be useful,
such edge-list should be saved into a file. The following command:</p>
<pre><code> $ ws 100 300 0.1 SHOW > ws_100_3_0.1.net
Rewired edges: 32
$
</code></pre>
<p>will save the resulting graph in the file <code>ws_100_3_0.1.net</code>. Notice
the usage of the symbol ">" to redirect the output of the program to
a file. The line printed on output reports the number of rewired
edges, since <code>SHOW</code> was specified as a fourth parameter.</p>
<h2 id="SEE-ALSO">SEE ALSO</h2>
<p><span class="man-ref">er_A<span class="s">(1)</span></span>, <span class="man-ref">er_B<span class="s">(1)</span></span></p>
<h2 id="REFERENCES">REFERENCES</h2>
<ul>
<li><p>D. J. Watts and S. H. Strogatz. "Collective dynamics of
'small-world' networks". Nature 393 (1998), 440–442.</p></li>
<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
Methods and Applications", Chapter 4, Cambridge University Press
(2017)</p></li>
</ul>
<h2 id="AUTHORS">AUTHORS</h2>
<p>(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <code><v.nicosia@qmul.ac.uk></code>.</p>
<ol class='man-decor man-foot man foot'>
<li class='tl'>www.complex-networks.net</li>
<li class='tc'>September 2017</li>
<li class='tr'>ws(1)</li>
</ol>
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