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