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.TH "F3M" "1" "September 2017" "www.complex-networks.net" "www.complex-networks.net"
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.SH "NAME"
\fBf3m\fR \- Count all the 3\-node subgraphs of a directed graph
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.SH "SYNOPSIS"
\fBf3m\fR \fIgraph_in\fR [\fInum_random\fR]
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.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\.
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.SH "PARAMETERS"
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.TP
\fIgraph_in\fR
input graph (edge list)\. It must be an existing file\.
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.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\.
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.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:
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.IP "" 4
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.nf

    motif_number  count  mean_rnd  std_rnd  z\-score
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.fi
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.IP "" 0
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.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:
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.IP "" 4
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.nf

   (count \- mean_rnd) / std_rnd
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.fi
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.IP "" 0
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.P
The program also prints a progress bar on STDERR\.
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.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:
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.IP "" 4
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.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_____/
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.fi
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.IP "" 0
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.SH "EXAMPLES"
To perform a motif analysis on the E\.coli transcription regulation graph, using 1000 randomised networks, we run the command:
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.IP "" 4
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.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
    $
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.fi
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.IP "" 0
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.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)\.
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.SH "SEE ALSO"
johnson_cycles(1)
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.SH "REFERENCES"
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.IP "\(bu" 4
R\. Milo et al\. "Network Motifs: Simple Building Blocks of Complex Networks"\. Science 298 (2002), 824\-827\.
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.IP "\(bu" 4
R\. Milo et al\. "Superfamilies of evolved and designed networks\." Science 303 (2004), 1538\-1542
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.IP "\(bu" 4
V\. Latora, V\. Nicosia, G\. Russo, "Complex Networks: Principles, Methods and Applications", Chapter 8, Cambridge University Press (2017)
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.IP "\(bu" 4
V\. Latora, V\. Nicosia, G\. Russo, "Complex Networks: Principles, Methods and Applications", Appendix 16, Cambridge University Press (2017)
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.IP "" 0
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.SH "AUTHORS"
(c) Vincenzo \'KatolaZ\' Nicosia 2009\-2017 \fB<v\.nicosia@qmul\.ac\.uk>\fR\.