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| author | KatolaZ <katolaz@freaknet.org> | 2017-09-27 15:06:31 +0100 |
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| committer | KatolaZ <katolaz@freaknet.org> | 2017-09-27 15:06:31 +0100 |
| commit | 3aee2fd43e3059a699af2b63c6f2395e5a55e515 (patch) | |
| tree | 58c95505a0906ed9cfa694f9dbd319403fd8f01d /doc/power_law.1.html | |
First commit on github -- NetBunch 1.0
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| -rw-r--r-- | doc/power_law.1.html | 217 |
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diff --git a/doc/power_law.1.html b/doc/power_law.1.html new file mode 100644 index 0000000..7ebae1c --- /dev/null +++ b/doc/power_law.1.html @@ -0,0 +1,217 @@ +<!DOCTYPE html> +<html> +<head> + <meta http-equiv='content-type' value='text/html;charset=utf8'> + <meta name='generator' value='Ronn/v0.7.3 (http://github.com/rtomayko/ronn/tree/0.7.3)'> + <title>power_law(1) - Sample N integers from a discrete power-law distribution</title> + <style type='text/css' media='all'> + /* style: man */ + body#manpage {margin:0} + .mp {max-width:100ex;padding:0 9ex 1ex 4ex} + .mp p,.mp pre,.mp ul,.mp ol,.mp dl {margin:0 0 20px 0} + .mp h2 {margin:10px 0 0 0} + .mp > p,.mp > pre,.mp > ul,.mp > ol,.mp > dl {margin-left:8ex} + .mp h3 {margin:0 0 0 4ex} + .mp dt {margin:0;clear:left} + .mp dt.flush {float:left;width:8ex} + .mp dd {margin:0 0 0 9ex} + .mp h1,.mp h2,.mp h3,.mp h4 {clear:left} + .mp pre {margin-bottom:20px} + .mp pre+h2,.mp pre+h3 {margin-top:22px} + .mp h2+pre,.mp h3+pre {margin-top:5px} + .mp img {display:block;margin:auto} + .mp h1.man-title {display:none} + .mp,.mp code,.mp pre,.mp tt,.mp kbd,.mp samp,.mp h3,.mp h4 {font-family:monospace;font-size:14px;line-height:1.42857142857143} + .mp h2 {font-size:16px;line-height:1.25} + .mp h1 {font-size:20px;line-height:2} + .mp {text-align:justify;background:#fff} + .mp,.mp code,.mp pre,.mp pre code,.mp tt,.mp kbd,.mp samp {color:#131211} + .mp h1,.mp h2,.mp h3,.mp h4 {color:#030201} + .mp u {text-decoration:underline} + .mp code,.mp strong,.mp b {font-weight:bold;color:#131211} + .mp em,.mp var {font-style:italic;color:#232221;text-decoration:none} + .mp a,.mp a:link,.mp a:hover,.mp a code,.mp a pre,.mp a tt,.mp a kbd,.mp a samp {color:#0000ff} + .mp b.man-ref {font-weight:normal;color:#434241} + .mp pre {padding:0 4ex} + .mp pre code {font-weight:normal;color:#434241} + .mp h2+pre,h3+pre {padding-left:0} + ol.man-decor,ol.man-decor li {margin:3px 0 10px 0;padding:0;float:left;width:33%;list-style-type:none;text-transform:uppercase;color:#999;letter-spacing:1px} + ol.man-decor {width:100%} + ol.man-decor li.tl {text-align:left} + ol.man-decor li.tc {text-align:center;letter-spacing:4px} + ol.man-decor li.tr {text-align:right;float:right} + </style> + <style type='text/css' media='all'> + /* style: toc */ + .man-navigation {display:block !important;position:fixed;top:0;left:113ex;height:100%;width:100%;padding:48px 0 0 0;border-left:1px solid #dbdbdb;background:#eee} + .man-navigation a,.man-navigation a:hover,.man-navigation a:link,.man-navigation a:visited {display:block;margin:0;padding:5px 2px 5px 30px;color:#999;text-decoration:none} + .man-navigation a:hover {color:#111;text-decoration:underline} + </style> +</head> +<!-- + The following styles are deprecated and will be removed at some point: + div#man, div#man ol.man, div#man ol.head, div#man ol.man. + + The .man-page, .man-decor, .man-head, .man-foot, .man-title, and + .man-navigation should be used instead. +--> +<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 <= k <= k_max, gamma < 1 +</code></pre> + +<p>The program can be used to generate a power-law degree distribution +with an assigned value of the exponent <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 > 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>> power_law -2.7 4 300 5000 > pl_-2.7_4_300_5000 +> $lastExitCode + +0 +> +</code></pre> + +<p>In this case, the exit code is <code>0</code>, meaning that the resulting set of +samples has an even sum (and can be thus used as a degree +sequence). Under Linux/MacOS/Unix (and in general when using any +POSIX-compliant shell) you should check the value of the variable +<code>$?</code>, right after executing <code>power_law</code>, i.e.:</p> + +<pre><code>$ power_law -2.5 3 500 5000 > 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><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'>power_law(1)</li> + </ol> + + </div> +</body> +</html> |