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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="#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>
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<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 > 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> <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 > 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 <span class="man-ref">ba<span class="s">(1)</span></span> 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>></code>).</p>
<h2 id="SEE-ALSO">SEE ALSO</h2>
<p><span class="man-ref">ba<span class="s">(1)</span></span>, <span class="man-ref">bb_fitness<span class="s">(1)</span></span></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><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'>dms(1)</li>
</ol>
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