diff options
Diffstat (limited to 'doc/conf_model_deg.1.html')
| -rw-r--r-- | doc/conf_model_deg.1.html | 190 |
1 files changed, 190 insertions, 0 deletions
diff --git a/doc/conf_model_deg.1.html b/doc/conf_model_deg.1.html new file mode 100644 index 0000000..c70ebdf --- /dev/null +++ b/doc/conf_model_deg.1.html @@ -0,0 +1,190 @@ +<!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>conf_model_deg(1) - Sample a simple graph from the configuration model</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'>conf_model_deg(1)</li> + <li class='tc'>www.complex-networks.net</li> + <li class='tr'>conf_model_deg(1)</li> + </ol> + + <h2 id="NAME">NAME</h2> +<p class="man-name"> + <code>conf_model_deg</code> - <span class="man-whatis">Sample a simple graph from the configuration model</span> +</p> + +<h2 id="SYNOPSIS">SYNOPSIS</h2> + +<p><code>conf_model_deg</code> <var>degs</var> [<var>threshold</var>]</p> + +<h2 id="DESCRIPTION">DESCRIPTION</h2> + +<p><code>conf_model_deg</code> samples a simple random undirected graph (i.e., a +graph without self-loops and multiple edges) from the configuration +model associated to the degree sequence provided in the input file +<var>degs</var>.</p> + +<h2 id="PARAMETERS">PARAMETERS</h2> + +<dl> +<dt class="flush"><var>degs</var></dt><dd><p> The name of the file containing the degree sequence. If <var>degs</var> is + equal to '-' (dash) the degree sequence is read from STDIN + (standard input).</p></dd> +<dt><var>threshold</var>:</dt><dd><p></p> + +<p> Optional number of edge stubs that are allowed to remain + unmatched. This is useful to create graphs from too-constrained + degree sequences (see <a href="#EXAMPLES" title="EXAMPLES" data-bare-link="true">EXAMPLES</a> below).</p></dd> +</dl> + + +<h2 id="OUTPUT">OUTPUT</h2> + +<p><code>conf_model_deg</code> prints on output the edge list of the sampled graph, +and reports on STDERR whether it has been able to find a graph.</p> + +<h2 id="EXAMPLES">EXAMPLES</h2> + +<p>Let us assume that the file <code>pl_-3.0_3_500_10000</code> contains a power-law +degree sequence ('gamma=-3.0', 'k_min=3', 'k_max=500', 'N=10000'), for +instance created using <a href="power_law.1.html">power_law(1)</a>. We can sample a +simple configuration model graph having that degree sequence using:</p> + +<pre><code> $ conf_model_deg pl_-3.0_3_500_10000 > conf_model_-3.0_3_500_10000.net +</code></pre> + +<p>where we have redirected the output (the resulting edge list) to the +file <code>conf_model_-3.0_3_500_10000.net</code>. In this case it is not +necessary to specify a threshold, since the maximum degree in the +sequence is 126, which is smaller than the structural cut-off.</p> + +<p>Let us assume now that the file <code>AS-20010316.net_degs</code> contains the +degree sequence of the data set <code>AS-20010316.net</code> (the graph of the +Internet at AS level in March 2001). In this case, the degree sequence +is too constrained, since the maximum degree (2277) is much larger +than the structural cut-off (see <a href="#REFERENCES" title="REFERENCES" data-bare-link="true">REFERENCES</a> below). So if we don't +specify a threshold, we get:</p> + +<pre><code> $ conf_model_deg AS-20010316.net_degs > AS_20010316_rand.net + Graph not found (unmatched stubs: 986 > threshold: 0) + Graph not found (unmatched stubs: 888 > threshold: 0) + Graph not found (unmatched stubs: 974 > threshold: 0) + ..... +</code></pre> + +<p>and so on, since <code>conf_model_deg</code> is trying to match all the edge +stubs, without success. From the messages printed by <code>conf_model_deg</code> +on STDERR we notice that the number of unmatched stubs is 986 in the +first attempt, 888 in the second one, and so on, while the acceptable +threshold is set to 0. If we instead specify a reasonable threshold +(in this example set to 950):</p> + +<pre><code> $ conf_model_deg AS-20010316.net_degs 950 > AS_20010316_rand.net + Graph not found (unmatched stubs: 978 > threshold: 950) + Found a graph (unmatched stubs: 876 <= threshold: 950) + $ +</code></pre> + +<p><code>conf_model_deg</code> is able to create a graph after a few +attempts. Notice that in the resulting graph 876 of the original edge +stubs will remain unmatched, meaning that the resulting graph has +876/2=438 edges less than those contained in the original graph.</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_nocheck.1.html">conf_model_deg_nocheck<span class="s">(1)</span></a>, <a class="man-ref" href="power_law.1.html">power_law<span class="s">(1)</span></a>, <a class="man-ref" href="hv_net.1.html">hv_net<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 12, 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'>conf_model_deg(1)</li> + </ol> + + </div> +</body> +</html> |