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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>dms(1) - Grow a scale-free random graph with tunable exponent</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="#OUTPUT">OUTPUT</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'>dms(1)</li>
+ <li class='tc'>www.complex-networks.net</li>
+ <li class='tr'>dms(1)</li>
+ </ol>
+
+ <h2 id="NAME">NAME</h2>
+<p class="man-name">
+ <code>dms</code> - <span class="man-whatis">Grow a scale-free random graph with tunable exponent</span>
+</p>
+
+<h2 id="SYNOPSIS">SYNOPSIS</h2>
+
+<p><code>dms</code> <var>N</var> <var>m</var> <var>n0</var> <em>a</em></p>
+
+<h2 id="DESCRIPTION">DESCRIPTION</h2>
+
+<p><code>dms</code> grows an undirected random scale-free graph with <var>N</var> nodes using
+the modified linear preferential attachment model proposed by
+Dorogovtsev, Mendes and Samukhin. The initial network is a clique of
+<var>n0</var> nodes, and each new node creates <var>m</var> new edges. The resulting
+graph will have a scale-free degree distribution, whose exponent
+converges to <code>gamma=3.0 + a/m</code> for large <var>N</var>.</p>
+
+<h2 id="PARAMETERS">PARAMETERS</h2>
+
+<dl>
+<dt class="flush"><var>N</var></dt><dd><p> Number of nodes of the final graph.</p></dd>
+<dt class="flush"><var>m</var></dt><dd><p> Number of edges created by each new node.</p></dd>
+<dt class="flush"><var>n0</var></dt><dd><p> Number of nodes in the initial (seed) graph.</p></dd>
+<dt class="flush"><em>a</em></dt><dd><p> This parameter sets the exponent of the degree distribution
+ (<code>gamma = 3.0 + a/m</code>). <em>a</em> must be larger than <var>-m</var>.</p></dd>
+</dl>
+
+
+<h2 id="OUTPUT">OUTPUT</h2>
+
+<p><code>dms</code> prints on STDOUT the edge list of the final graph.</p>
+
+<h2 id="EXAMPLES">EXAMPLES</h2>
+
+<p>Let us assume that we want to create a scale-free network with
+<var>N=10000</var> nodes, with average degree equal to 8, whose degree
+distribution has exponent</p>
+
+<pre><code> gamma = 2.5
+</code></pre>
+
+<p>Since <code>dms</code> produces graphs with scale-free degree sequences with an
+exponent <code>gamma = 3.0 + a/m</code>, the command:</p>
+
+<pre><code> $ dms 10000 4 4 -2.0 &gt; dms_10000_4_4_-2.0.txt
+</code></pre>
+
+<p>will produce the desired network. In fact, the average degree of the
+graph will be:</p>
+
+<pre><code> &lt;k> = 2m = 8
+</code></pre>
+
+<p>and the exponent of the power-law degree distribution will be:</p>
+
+<pre><code> gamma = 3.0 + a/m = 3.0 -0.5 = 2.5
+</code></pre>
+
+<p>The following command:</p>
+
+<pre><code> $ dms 10000 3 5 0 &gt; dms_10000_3_5_0.txt
+</code></pre>
+
+<p>creates a scale-free graph with <var>N=10000</var> nodes, where each new node
+creates <var>m=3</var> new edges and the initial seed network is a ring of
+<var>n0=5</var> nodes. The degree distribution of the final graph will have
+exponent equal to <code>gamma = 3.0 + a/m = 3.0</code>. In this case, <code>dms</code>
+produces a Barabasi-Albert graph (see <a class="man-ref" href="ba.1.html">ba<span class="s">(1)</span></a> for details). The edge
+list of the graph is saved in the file <code>dms_10000_3_5_0.txt</code> (thanks
+to the redirection operator <code>&gt;</code>).</p>
+
+<h2 id="SEE-ALSO">SEE ALSO</h2>
+
+<p><a class="man-ref" href="ba.1.html">ba<span class="s">(1)</span></a>, <a class="man-ref" href="bb_fitness.1.html">bb_fitness<span class="s">(1)</span></a></p>
+
+<h2 id="REFERENCES">REFERENCES</h2>
+
+<ul>
+<li><p>S. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin. "Structure of
+ Growing Networks with Preferential Linking". Phys. Rev. Lett. 85
+ (2000), 4633-4636.</p></li>
+<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
+Methods and Applications", Chapter 6, Cambridge University Press
+(2017)</p></li>
+<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
+Methods and Applications", Appendix 13, 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'>dms(1)</li>
+ </ol>
+
+ </div>
+</body>
+</html>