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<title>bb_fitness(1) - Grow a random graph with the fitness model</title>
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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'>bb_fitness(1)</li>
<li class='tc'>www.complex-networks.net</li>
<li class='tr'>bb_fitness(1)</li>
</ol>
<h2 id="NAME">NAME</h2>
<p class="man-name">
<code>bb_fitness</code> - <span class="man-whatis">Grow a random graph with the fitness model</span>
</p>
<h2 id="SYNOPSIS">SYNOPSIS</h2>
<p><code>bb_fitness</code> <var>N</var> <var>m</var> <var>n0</var> [SHOW]</p>
<h2 id="DESCRIPTION">DESCRIPTION</h2>
<p><code>bb_fitness</code> grows an undirected random scale-free graph with <var>N</var>
nodes using the fitness model proposed by Bianconi and Barabasi. The
initial network is a clique of <var>n0</var> nodes, and each new node creates
<var>m</var> new edges. The probability that a new node create an edge to node
<code>j</code> is proportional to</p>
<pre><code> a_j * k_j
</code></pre>
<p>where <code>a_j</code> is the attractiveness (fitness) of node <code>j</code>. The values of
node attractiveness are sampled uniformly in the interval [0,1].</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">SHOW</dt><dd><p> If the fourth parameter is equal to <code>SHOW</code>, the values of node
attractiveness are printed on STDERR.</p></dd>
</dl>
<h2 id="OUTPUT">OUTPUT</h2>
<p><code>bb_fitness</code> prints on STDOUT the edge list of the final graph.</p>
<h2 id="EXAMPLES">EXAMPLES</h2>
<p>The following command:</p>
<pre><code> $ bb_fitness 10000 3 4 > bb_fitness_10000_3_4.txt
</code></pre>
<p>uses the fitness model to create a random 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 edge list of the resulting
graph is saved in the file <code>bb_fitness_10000_3_4.txt</code> (notice the
redirection operator <code>></code>). The command:</p>
<pre><code> $ bb_fitness 10000 3 4 SHOW > bb_fitness_10000_3_4.txt 2> bb_fitness_10000_3_4.txt_fitness
</code></pre>
<p>will do the same as above, but it will additionally save the values of
node fitness in the file <code>bb_fitness_10000_3_4.txt_fitness</code> (notice
the redirection operator <code>2></code>, that redirects the STDERR to the
specified file).</p>
<h2 id="SEE-ALSO">SEE ALSO</h2>
<p><span class="man-ref">ba<span class="s">(1)</span></span>, <span class="man-ref">dms<span class="s">(1)</span></span></p>
<h2 id="REFERENCES">REFERENCES</h2>
<ul>
<li><p>G. Bianconi, A.-L. Barabasi, " Competition and multiscaling in
evolving networks". EPL-Europhys. Lett. 54 (2001), 436.</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'>bb_fitness(1)</li>
</ol>
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