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diff --git a/doc/knn.1.html b/doc/knn.1.html new file mode 100644 index 0000000..c8ea160 --- /dev/null +++ b/doc/knn.1.html @@ -0,0 +1,239 @@ +<!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>knn(1) - Compute the average nearest neighbours degree function</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="#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'>knn(1)</li> + <li class='tc'>www.complex-networks.net</li> + <li class='tr'>knn(1)</li> + </ol> + + <h2 id="NAME">NAME</h2> +<p class="man-name"> + <code>knn</code> - <span class="man-whatis">Compute the average nearest neighbours degree function</span> +</p> + +<h2 id="SYNOPSIS">SYNOPSIS</h2> + +<p><code>knn</code> <var>graph_in</var> [<var>NO|LIN|EXP</var> <var>bin_param</var>]</p> + +<h2 id="DESCRIPTION">DESCRIPTION</h2> + +<p><code>knn</code> computes the average nearest neighbours degree function knn(k) +of the graph <var>graph_in</var> given as input. The program can (optionally) +average the results over bins of equal or exponentially increasing +width (the latter is also known as logarithmic binning).</p> + +<h2 id="PARAMETERS">PARAMETERS</h2> + +<dl> +<dt><var>graph_in</var></dt><dd><p> undirected input graph (edge list). If is equal to <code>-</code> (dash), read + the edge list from STDIN.</p></dd> +<dt class="flush">NO</dt><dd><p> If the second (optional) parameter is equal to <code>NO</code>, or omitted, + the program will print on output the values of knn(k) for all the + degrees in <var>graph_in</var>.</p></dd> +<dt class="flush">LIN</dt><dd><p> If the second (optional) parameter is equal to <code>LIN</code>, the program + will average the values of knn(k) over <var>bin_param</var> bins of equal + length.</p></dd> +<dt class="flush">EXP</dt><dd><p> If the second (optional) parameter is equal to <code>EXP</code>, the progam + will average the values of knn(k) over bins of exponentially + increasing width (also known as 'logarithmic binning', which is + odd, since the width of subsequent bins increases exponentially, + not logarithmically, but there you go...). In this case, + <var>bin_param</var> is the exponent of the increase.</p></dd> +<dt><var>bin_param</var></dt><dd><p> If the second parameter is equal to <code>LIN</code>, <var>bin_param</var> is the + number of bins used in the linear binning. If the second parameter + is <code>EXP</code>, <var>bin_param</var> is the exponent used to determine the width + of each bin.</p></dd> +</dl> + + +<h2 id="OUTPUT">OUTPUT</h2> + +<p>The output is in the form:</p> + +<pre><code> k1 knn(k1) + k2 knn(k2) + .... +</code></pre> + +<p>If no binning is selected, <code>k1</code>, <code>k2</code>, etc. are the degrees observed +in <var>graph_in</var>. If linear or exponential binning is required, then +<code>k1</code>, <code>k2</code>, etc. are the right extremes of the corresponding bin.</p> + +<h2 id="EXAMPLES">EXAMPLES</h2> + +<p>To compute the average neanest-neighbours degree function for a given +graph we just run:</p> + +<pre><code> $ knn er_1000_5000.net + 2 10.5 + 3 11.333333 + 4 10.785714 + 5 11.255319 + 6 11.336601 + 7 11.176292 + 8 11.067568 + 9 11.093519 + 10 10.898438 + 11 10.906009 + 12 11.031353 + 13 10.73938 + 14 10.961538 + 15 10.730864 + 16 10.669118 + 17 10.702206 + 18 10.527778 + 19 11.302632 + 20 11.8 + $ +</code></pre> + +<p>Since we have not requested a binning, the program will output the +value of knn(k) for each of the degrees actually observed in the graph +<code>er_1000_5000.net</code> (the mininum degree is 2 and the maximum degree is +20). Notice that in this case, as expected in a graph without +degree-degree correlations, the values of knn(k) are almost +independent of k.</p> + +<p>We can also ask <code>knn</code> to bin the results over 5 bins of equal width by +running:</p> + +<pre><code> $ knn er_1000_5000.net LIN 5 + 6 11.249206 + 10 11.037634 + 14 10.919366 + 18 10.68685 + 22 11.474138 + $ +</code></pre> + +<p>Let us consider the case of <code>movie_actors.net</code>, i.e. the actors +collaboration network. Here we ask <code>knn</code> to compute the average +nearest-neighbours degrees using exponential binning:</p> + +<pre><code> $ knn movie_actors.net EXP 1.4 + 2 142.56552 + 5 129.09559 + 9 158.44493 + 15 198.77922 + 23 205.96538 + 34 210.07379 + 50 227.57167 + 72 235.89857 + 102 254.47583 + 144 276.572 + 202 307.11004 + 283 337.83733 + 397 370.34222 + 556 410.89117 + 779 446.66331 + 1091 498.73118 + 1527 547.31923 + 2137 577.87852 + 2991 582.6855 + 4187 557.44801 + $ +</code></pre> + +<p>Notice that, due to the presence of the second parameter <code>EXP</code>, the +program has printed on output knn(k) over bins of exponentially +increasing width, using an exponent <code>1.4</code>. This is useful for plotting +with log or semilog axes. In this case, the clear increasing trend of +knn(k) indicates the presence of assortative correlations.</p> + +<h2 id="SEE-ALSO">SEE ALSO</h2> + +<p><a class="man-ref" href="knn_w.1.html">knn_w<span class="s">(1)</span></a>, <a class="man-ref" href="deg_seq.1.html">deg_seq<span class="s">(1)</span></a></p> + +<h2 id="REFERENCES">REFERENCES</h2> + +<ul> +<li>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, +Methods and Applications", Chapter 7, Cambridge University Press +(2017)</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'>knn(1)</li> + </ol> + + </div> +</body> +</html> |