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