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authorKatolaZ <katolaz@freaknet.org>2017-09-27 15:06:31 +0100
committerKatolaZ <katolaz@freaknet.org>2017-09-27 15:06:31 +0100
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+ <title>ws(1) - Create a small-world graph using the Watts-Strogatz model</title>
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+<body id='manpage'>
+ <div class='mp' id='man'>
+
+ <div class='man-navigation' style='display:none'>
+ <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>
+ </div>
+
+ <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>
+ </ol>
+
+ <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 &gt; 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><a class="man-ref" href="er_A.1.html">er_A<span class="s">(1)</span></a>, <a class="man-ref" href="er_B.1.html">er_B<span class="s">(1)</span></a></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>&lt;v.nicosia@qmul.ac.uk&gt;</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>
+
+ </div>
+</body>
+</html>