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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(1) - Compute the average nearest neighbours degree function</title>
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+ <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>&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(1)</li>
+ </ol>
+
+ </div>
+</body>
+</html>
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