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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>
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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="#OUTPUT">OUTPUT</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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</div>
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<ol class='man-decor man-head man head'>
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<li class='tl'>bb_fitness(1)</li>
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<li class='tc'>www.complex-networks.net</li>
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<li class='tr'>bb_fitness(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>bb_fitness</code> - <span class="man-whatis">Grow a random graph with the fitness model</span>
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</p>
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<h2 id="SYNOPSIS">SYNOPSIS</h2>
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<p><code>bb_fitness</code> <var>N</var> <var>m</var> <var>n0</var> [SHOW]</p>
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<h2 id="DESCRIPTION">DESCRIPTION</h2>
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<p><code>bb_fitness</code> grows an undirected random scale-free graph with <var>N</var>
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nodes using the fitness model proposed by Bianconi and Barabasi. The
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initial network is a clique of <var>n0</var> nodes, and each new node creates
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<var>m</var> new edges. The probability that a new node create an edge to node
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<code>j</code> is proportional to</p>
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<pre><code> a_j * k_j
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</code></pre>
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<p>where <code>a_j</code> is the attractiveness (fitness) of node <code>j</code>. The values of
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node attractiveness are sampled uniformly in the interval [0,1].</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 of the final graph.</p></dd>
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<dt class="flush"><var>m</var></dt><dd><p> Number of edges created by each new node.</p></dd>
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<dt class="flush"><var>n0</var></dt><dd><p> Number of nodes in the initial (seed) graph.</p></dd>
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<dt class="flush">SHOW</dt><dd><p> If the fourth parameter is equal to <code>SHOW</code>, the values of node
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attractiveness are printed on STDERR.</p></dd>
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</dl>
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<h2 id="OUTPUT">OUTPUT</h2>
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<p><code>bb_fitness</code> prints on STDOUT the edge list of the final graph.</p>
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<h2 id="EXAMPLES">EXAMPLES</h2>
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<p>The following command:</p>
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<pre><code> $ bb_fitness 10000 3 4 > bb_fitness_10000_3_4.txt
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</code></pre>
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<p>uses the fitness model to create a random graph with <var>N=10000</var> nodes,
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where each new node creates <var>m=3</var> new edges and the initial seed
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network is a ring of <var>n0=5</var> nodes. The edge list of the resulting
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graph is saved in the file <code>bb_fitness_10000_3_4.txt</code> (notice the
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redirection operator <code>></code>). The command:</p>
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<pre><code> $ bb_fitness 10000 3 4 SHOW > bb_fitness_10000_3_4.txt 2> bb_fitness_10000_3_4.txt_fitness
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</code></pre>
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<p>will do the same as above, but it will additionally save the values of
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node fitness in the file <code>bb_fitness_10000_3_4.txt_fitness</code> (notice
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the redirection operator <code>2></code>, that redirects the STDERR to the
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specified file).</p>
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<h2 id="SEE-ALSO">SEE ALSO</h2>
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<p><span class="man-ref">ba<span class="s">(1)</span></span>, <span class="man-ref">dms<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>G. Bianconi, A.-L. Barabasi, " Competition and multiscaling in
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evolving networks". EPL-Europhys. Lett. 54 (2001), 436.</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 6, Cambridge University Press
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(2017)</p></li>
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<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
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Methods and Applications", Appendix 13, 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'>bb_fitness(1)</li>
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</ol>
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</body>
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