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.\" generated with Ronn/v0.7.3
.\" http://github.com/rtomayko/ronn/tree/0.7.3
.
.TH "F3M" "1" "September 2017" "www.complex-networks.net" "www.complex-networks.net"
.
.SH "NAME"
\fBf3m\fR \- Count all the 3\-node subgraphs of a directed graph
.
.SH "SYNOPSIS"
\fBf3m\fR \fIgraph_in\fR [\fInum_random\fR]
.
.SH "DESCRIPTION"
\fBf3m\fR performs a motif analysis on \fIgraph_in\fR, 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\.
.
.SH "PARAMETERS"
.
.TP
\fIgraph_in\fR
input graph (edge list)\. It must be an existing file\.
.
.TP
\fInum_random\fR
The number of random graphs to sample from the configuration model for the computation of the z\-score of the motifs\.
.
.SH "OUTPUT"
\fBf3m\fR 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:
.
.IP "" 4
.
.nf
motif_number count mean_rnd std_rnd z\-score
.
.fi
.
.IP "" 0
.
.P
where \fBmotif_number\fR is a number between 1 and 13 that identifies the motif (see \fIMOTIF NUMBERS\fR below), \fBcount\fR is the number of subgraphs ot type \fBmotif_number\fR found in \fIgraph_in\fR, \fBmean_rnd\fR is the average number of subgraphs of type \fBmotif_number\fR in the corresponding configuration model ensemble, and \fBstd_rnd\fR is the associated standard deviation\. Finally, \fBz\-score\fR is the quantity:
.
.IP "" 4
.
.nf
(count \- mean_rnd) / std_rnd
.
.fi
.
.IP "" 0
.
.P
The program also prints a progress bar on STDERR\.
.
.SH "MOTIF NUMBERS"
We report below the correspondence between the 13 possible 3\-node subgraphs and the corresponding \fBmotif_number\fR\. In the diagrams, \'O\-\-\->O\' indicates a single edge form the left node to the right node, while \'O\fI==\fRO\' indicates a double (bi\-directional) edge between the two nodes:
.
.IP "" 4
.
.nf
(1) O<\-\-\-O\-\-\->O
(2) O\-\-\->O\-\-\->O
(3) O<==>O\-\-\->O
(4) O\-\-\->O<\-\-\-O
(5) O\-\-\->O\-\-\->O
\e ^
\e_______|
(6) O<==>O\-\-\->O
\e ^
\e_______|
(7) O<==>O<\-\-\-O
(8) O<==>O<==>O
(9) O<\-\-\-O<\-\-\-O
\e ^
\e_______|
(10) O<==>O<\-\-\-O
\e ^
\e_______|
(11) O\-\-\->O<==>O
\e ^
\e_______|
(12) O<==>O<==>O
\e ^
\e_______|
(13) O<==>O<==>O
^\e ^/
\e\e_____//
\e_____/
.
.fi
.
.IP "" 0
.
.SH "EXAMPLES"
To perform a motif analysis on the E\.coli transcription regulation graph, using 1000 randomised networks, we run the command:
.
.IP "" 4
.
.nf
$ 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
$
.
.fi
.
.IP "" 0
.
.P
Notice that the motif \fB5\fR (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 \fB2\fR (three\-node chain) is underrepresented, as made evident by value of the z\-score (\-3\.338)\.
.
.SH "SEE ALSO"
johnson_cycles(1)
.
.SH "REFERENCES"
.
.IP "\(bu" 4
R\. Milo et al\. "Network Motifs: Simple Building Blocks of Complex Networks"\. Science 298 (2002), 824\-827\.
.
.IP "\(bu" 4
R\. Milo et al\. "Superfamilies of evolved and designed networks\." Science 303 (2004), 1538\-1542
.
.IP "\(bu" 4
V\. Latora, V\. Nicosia, G\. Russo, "Complex Networks: Principles, Methods and Applications", Chapter 8, Cambridge University Press (2017)
.
.IP "\(bu" 4
V\. Latora, V\. Nicosia, G\. Russo, "Complex Networks: Principles, Methods and Applications", Appendix 16, Cambridge University Press (2017)
.
.IP "" 0
.
.SH "AUTHORS"
(c) Vincenzo \'KatolaZ\' Nicosia 2009\-2017 \fB<v\.nicosia@qmul\.ac\.uk>\fR\.
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