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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>knn_w(1) - Compute the weighted average nearest neighbours degree function</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="#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_w(1)</li>
+ <li class='tc'>www.complex-networks.net</li>
+ <li class='tr'>knn_w(1)</li>
+ </ol>
+
+ <h2 id="NAME">NAME</h2>
+<p class="man-name">
+ <code>knn_w</code> - <span class="man-whatis">Compute the weighted average nearest neighbours degree function</span>
+</p>
+
+<h2 id="SYNOPSIS">SYNOPSIS</h2>
+
+<p><code>knn_w</code> <var>graph_in</var> [<var>NO|LIN|EXP</var> <var>bin_param</var>]</p>
+
+<h2 id="DESCRIPTION">DESCRIPTION</h2>
+
+<p><code>knn_w</code> computes the weighted average nearest neighbours degree
+function knn_w(k) of the weighted 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 and weighted 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_w(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_w(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_w(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_w(k1)
+ k2 knn_w(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 of the US
+air transportation network we can run:</p>
+
+<pre><code> $ knn_w US_airports.net
+ 1 81.8
+ 2 30.350938
+ 3 15.198846
+ 4 15.046341
+ 5 13.967998
+ 6 16.293341
+ 7 11.746223
+ 8 11.53912
+ 9 7.9134643
+ 10 8.317504
+ ....
+ 132 0.46248989
+ 136 0.47312661
+ 145 0.37386548
+ $
+</code></pre>
+
+<p>Since we have not requested a binning, the program will output the
+value of knn_w(k) for each of the degrees actually observed in the
+input graph (the mininum degree is 1 and the maximum degree is
+145). We can also ask <code>knn_w</code> to bin the results over 10 bins of equal
+width by running:</p>
+
+<pre><code> $ knn_w US_airports.net 10
+ 16 68.359133
+ 31 89.519255
+ 46 78.911709
+ 61 78.802765
+ 76 76.352358
+ 91 71.589354
+ 106 60.433329
+ 121 62.600988
+ 136 64.81641
+ 151 54.210494
+ $
+</code></pre>
+
+<p>or to use instead an exponential binning:</p>
+
+<pre><code> $ knn_w US_airports.net EXP 1.3
+ 3 63.062388
+ 6 70.319368
+ 10 81.856768
+ 15 79.766008
+ 21 96.172011
+ 29 84.771533
+ 39 79.591139
+ 52 80.222237
+ 69 79.776163
+ 91 72.217712
+ 119 61.878435
+ 155 62.695227
+ $
+</code></pre>
+
+<h2 id="SEE-ALSO">SEE ALSO</h2>
+
+<p><a class="man-ref" href="knn.1.html">knn<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><p>A. Barrat et al. "The architecture of complex weighted
+networks". P. Natl. Acad. Sci USA 101 (2004), 3747-3752.</p></li>
+<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
+Methods and Applications", Chapter 10, 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'>knn_w(1)</li>
+ </ol>
+
+ </div>
+</body>
+</html>
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