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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>power_law(1) - Sample N integers from a discrete power-law distribution</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="#RETURN-VALUES">RETURN VALUES</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'>power_law(1)</li>
+ <li class='tc'>www.complex-networks.net</li>
+ <li class='tr'>power_law(1)</li>
+ </ol>
+
+ <h2 id="NAME">NAME</h2>
+<p class="man-name">
+ <code>power_law</code> - <span class="man-whatis">Sample N integers from a discrete power-law distribution</span>
+</p>
+
+<h2 id="SYNOPSIS">SYNOPSIS</h2>
+
+<p><code>power_law</code> <var>gamma</var> <var>k_min</var> <var>k_max</var> <var>N</var></p>
+
+<h2 id="DESCRIPTION">DESCRIPTION</h2>
+
+<p><code>power_law</code> samples <var>N</var> elements from the discrete power-law
+distribution</p>
+
+<pre><code>P(k) ~ k^{gamma}
+</code></pre>
+
+<p>where</p>
+
+<pre><code>k_min &lt;= k &lt;= k_max, gamma &lt; 1
+</code></pre>
+
+<p>The program can be used to generate a power-law degree distribution
+with an assigned value of the exponent &lt;gamma.</p>
+
+<h2 id="PARAMETERS">PARAMETERS</h2>
+
+<ul>
+<li><p><var>gamma</var>:
+ Exponent of the power-law distribution.</p></li>
+<li><p><var>k_min</var>, <var>k_max</var>:
+ Boundaries of the sampling interval.</p></li>
+<li><p><var>N</var>
+ The number of samples to generate</p></li>
+</ul>
+
+
+<h2 id="OUTPUT">OUTPUT</h2>
+
+<p><code>power_law</code> prints on the standard output the sampled values, one per
+line, in the format:</p>
+
+<pre><code>s1
+s2
+s3
+ ...
+sN
+</code></pre>
+
+<p>The program returns the value <code>0</code> if the sum of the samples is even,
+or returns <code>1</code> otherwise. The return value can be used to determine
+whether the set of samples can correspond to a degree sequence (if the
+sum of the sequence is odd, then the sequence cannot be a valid degree
+sequence). See <a href="#RETURN-VALUES" title="RETURN VALUES" data-bare-link="true">RETURN VALUES</a> below.</p>
+
+<h2 id="EXAMPLES">EXAMPLES</h2>
+
+<p>To generate <var>N=1000</var> independent samples from the power-law
+distribution <code>P(k) ~ k^(-3)</code>, where samples are in the interval
+<code>[3, 50]</code>, we can use:</p>
+
+<pre><code>$ power_law -3.0 3 50 1000
+11
+3
+3
+5
+6
+7
+ ....
+8
+3
+$
+</code></pre>
+
+<p>To save the samples in the file <code>pl_-3.0_3_50_1000</code>, we redirect STDOUT:</p>
+
+<pre><code>$ power_law -3.0 3 50 1000 &gt; pl_-3.0_3_50_1000
+</code></pre>
+
+<h2 id="RETURN-VALUES">RETURN VALUES</h2>
+
+<p>The value returned by <code>power_law</code> can be used to test whether the sum
+of the resulting set of samples is even or odd. Under Windows
+PowerShell, you can check the last exit code by inspecting the
+variable <code>$lastExitCode</code> right after executing <code>power_law</code>, as in:</p>
+
+<pre><code>&gt; power_law -2.7 4 300 5000 &gt; pl_-2.7_4_300_5000
+&gt; $lastExitCode
+
+0
+&gt;
+</code></pre>
+
+<p>In this case, the exit code is <code>0</code>, meaning that the resulting set of
+samples has an even sum (and can be thus used as a degree
+sequence). Under Linux/MacOS/Unix (and in general when using any
+POSIX-compliant shell) you should check the value of the variable
+<code>$?</code>, right after executing <code>power_law</code>, i.e.:</p>
+
+<pre><code>$ power_law -2.5 3 500 5000 &gt; pl_-2.5_3_500_5000
+$ echo $?
+1
+$
+</code></pre>
+
+<p>Notice that this particular run of <code>power_law</code> has produced a sequence
+with an odd sum, which thus cannot correspond to a valid degree sequence.</p>
+
+<h2 id="SEE-ALSO">SEE ALSO</h2>
+
+<p><a class="man-ref" href="deg_seq.1.html">deg_seq<span class="s">(1)</span></a>, <a class="man-ref" href="conf_model_deg.1.html">conf_model_deg<span class="s">(1)</span></a>, <a class="man-ref" href="conf_model_deg_nocheck.1.html">conf_model_deg_nocheck<span class="s">(1)</span></a></p>
+
+<h2 id="REFERENCES">REFERENCES</h2>
+
+<ul>
+<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
+Methods and Applications", Chapter 5, Cambridge University Press
+(2017)</p></li>
+<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
+Methods and Applications", Appendix 9, 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'>power_law(1)</li>
+ </ol>
+
+ </div>
+</body>
+</html>