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<title>f3m(1) - Count all the 3-node subgraphs of a directed graph</title>
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<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>
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<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>
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<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<---O--->O
(2) O--->O--->O
(3) O<==>O--->O
(4) O--->O<---O
(5) O--->O--->O
\ ^
\_______|
(6) O<==>O--->O
\ ^
\_______|
(7) O<==>O<---O
(8) O<==>O<==>O
(9) O<---O<---O
\ ^
\_______|
(10) O<==>O<---O
\ ^
\_______|
(11) O--->O<==>O
\ ^
\_______|
(12) O<==>O<==>O
\ ^
\_______|
(13) O<==>O<==>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><span class="man-ref">johnson_cycles<span class="s">(1)</span></span></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><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'>f3m(1)</li>
</ol>
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