f3m - Count all the 3-node subgraphs of a directed graph
f3m graph_in [num_random]
f3m performs a motif analysis on graph_in, 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.
input graph (edge list). It must be an existing file.
The number of random graphs to sample from the configuration model for the computation of the z-score of the motifs.
f3m 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:
motif_number count mean_rnd std_rnd z-score
where motif_number is a number between 1 and 13 that identifies the
motif (see MOTIF NUMBERS below), count is the number of
subgraphs ot type motif_number found in graph_in, mean_rnd is
the average number of subgraphs of type motif_number in the
corresponding configuration model ensemble, and std_rnd is the
associated standard deviation. Finally, z-score is the quantity:
(count - mean_rnd) / std_rnd
The program also prints a progress bar on STDERR.
We report below the correspondence between the 13 possible 3-node
subgraphs and the corresponding motif_number. In the diagrams,
'O--->O' indicates a single edge form the left node to the right node,
while 'O==O' indicates a double (bi-directional) edge between the
two nodes:
(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
^\ ^/
\\_____//
\_____/
To perform a motif analysis on the E.coli transcription regulation graph, using 1000 randomised networks, we run the command:
$ 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
$
Notice that the motif 5 (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 2 (three-node chain) is
underrepresented, as made evident by value of the z-score (-3.338).
R. Milo et al. "Network Motifs: Simple Building Blocks of Complex Networks". Science 298 (2002), 824-827.
R. Milo et al. "Superfamilies of evolved and designed networks." Science 303 (2004), 1538-1542
V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, Methods and Applications", Chapter 8, Cambridge University Press (2017)
V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, Methods and Applications", Appendix 16, Cambridge University Press (2017)
(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <v.nicosia@qmul.ac.uk>.