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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>f3m(1) - Count all the 3-node subgraphs of a directed graph</title>
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+
+ <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="#MOTIF-NUMBERS">MOTIF NUMBERS</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'>f3m(1)</li>
+ <li class='tc'>www.complex-networks.net</li>
+ <li class='tr'>f3m(1)</li>
+ </ol>
+
+ <h2 id="NAME">NAME</h2>
+<p class="man-name">
+ <code>f3m</code> - <span class="man-whatis">Count all the 3-node subgraphs of a directed graph</span>
+</p>
+
+<h2 id="SYNOPSIS">SYNOPSIS</h2>
+
+<p><code>f3m</code> <var>graph_in</var> [<var>num_random</var>]</p>
+
+<h2 id="DESCRIPTION">DESCRIPTION</h2>
+
+<p><code>f3m</code> performs a motif analysis on <var>graph_in</var>, i.e., it counts all the
+3-node subgraphs and computes the z-score of that count with respect
+to the corresponding configuration model ensemble.</p>
+
+<h2 id="PARAMETERS">PARAMETERS</h2>
+
+<dl>
+<dt><var>graph_in</var></dt><dd><p> input graph (edge list). It must be an existing file.</p></dd>
+<dt><var>num_random</var></dt><dd><p> The number of random graphs to sample from the configuration model
+ for the computation of the z-score of the motifs.</p></dd>
+</dl>
+
+
+<h2 id="OUTPUT">OUTPUT</h2>
+
+<p><code>f3m</code> prints on the standard output a table with 13 rows, one for each
+of the 13 possible 3-node motifs. Each line is in the format:</p>
+
+<pre><code> motif_number count mean_rnd std_rnd z-score
+</code></pre>
+
+<p>where <code>motif_number</code> is a number between 1 and 13 that identifies the
+motif (see <a href="#MOTIF-NUMBERS" title="MOTIF NUMBERS" data-bare-link="true">MOTIF NUMBERS</a> below), <code>count</code> is the number of
+subgraphs ot type <code>motif_number</code> found in <var>graph_in</var>, <code>mean_rnd</code> is
+the average number of subgraphs of type <code>motif_number</code> in the
+corresponding configuration model ensemble, and <code>std_rnd</code> is the
+associated standard deviation. Finally, <code>z-score</code> is the quantity:</p>
+
+<pre><code> (count - mean_rnd) / std_rnd
+</code></pre>
+
+<p>The program also prints a progress bar on STDERR.</p>
+
+<h2 id="MOTIF-NUMBERS">MOTIF NUMBERS</h2>
+
+<p>We report below the correspondence between the 13 possible 3-node
+subgraphs and the corresponding <code>motif_number</code>. In the diagrams,
+'O--->O' indicates a single edge form the left node to the right node,
+while 'O<var>==</var>O' indicates a double (bi-directional) edge between the
+two nodes:</p>
+
+<pre><code> (1) O&lt;---O--->O
+
+ (2) O---&gt;O---&gt;O
+
+ (3) O&lt;==>O---&gt;O
+
+ (4) O---&gt;O&lt;---O
+
+ (5) O--->O---&gt;O
+ \ ^
+ \_______|
+
+ (6) O&lt;==>O---&gt;O
+ \ ^
+ \_______|
+
+ (7) O&lt;==>O&lt;---O
+
+ (8) O&lt;==>O&lt;==>O
+
+ (9) O&lt;---O&lt;---O
+ \ ^
+ \_______|
+
+ (10) O&lt;==>O&lt;---O
+ \ ^
+ \_______|
+
+ (11) O--->O&lt;==>O
+ \ ^
+ \_______|
+
+ (12) O&lt;==>O&lt;==>O
+ \ ^
+ \_______|
+
+ (13) O&lt;==>O&lt;==>O
+ ^\ ^/
+ \\_____//
+ \_____/
+</code></pre>
+
+<h2 id="EXAMPLES">EXAMPLES</h2>
+
+<p>To perform a motif analysis on the E.coli transcription regulation
+graph, using 1000 randomised networks, we run the command:</p>
+
+<pre><code> $ f3m e_coli.net 1000
+ 1 4760 4400.11 137.679 +2.614
+ 2 162 188.78 8.022 -3.338
+ 3 0 0.89 3.903 -0.228
+ 4 226 238.32 7.657 -1.609
+ 5 40 6.54 2.836 +11.800
+ 6 0 0.01 0.077 -0.078
+ 7 0 0.12 0.642 -0.192
+ 8 0 0.00 0.032 -0.032
+ 9 0 0.01 0.109 -0.110
+ 10 0 0.00 0.000 +0.000
+ 11 0 0.00 0.032 -0.032
+ 12 0 0.00 0.000 +0.000
+ 13 0 0.00 0.000 +0.000
+ $
+</code></pre>
+
+<p>Notice that the motif <code>5</code> (the so-called "feed-forward loop") has a
+z-score equal to 11.8, meaning that it is highly overrepresented in
+the E.coli graph with respect to the corresponding configuration model
+ensemble. Conversely, the motif <code>2</code> (three-node chain) is
+underrepresented, as made evident by value of the z-score (-3.338).</p>
+
+<h2 id="SEE-ALSO">SEE ALSO</h2>
+
+<p><a class="man-ref" href="johnson_cycles.1.html">johnson_cycles<span class="s">(1)</span></a></p>
+
+<h2 id="REFERENCES">REFERENCES</h2>
+
+<ul>
+<li><p>R. Milo et al. "Network Motifs: Simple Building Blocks of Complex
+Networks". Science 298 (2002), 824-827.</p></li>
+<li><p>R. Milo et al. "Superfamilies of evolved and designed networks."
+Science 303 (2004), 1538-1542</p></li>
+<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
+Methods and Applications", Chapter 8, Cambridge University Press
+(2017)</p></li>
+<li><p>V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
+Methods and Applications", Appendix 16, 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'>f3m(1)</li>
+ </ol>
+
+ </div>
+</body>
+</html>