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f3m(1) -- Count all the 3-node subgraphs of a directed graph
======
## SYNOPSIS
`f3m` <graph_in> [<num_random>]
## DESCRIPTION
`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.
## PARAMETERS
* <graph_in>:
input graph (edge list). It must be an existing file.
* <num_random>:
The number of random graphs to sample from the configuration model
for the computation of the z-score of the motifs.
## OUTPUT
`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.
## MOTIF NUMBERS
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
^\ ^/
\\_____//
\_____/
## EXAMPLES
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).
## SEE ALSO
johnson_cycles(1)
## REFERENCES
* 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)
## AUTHORS
(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 `<v.nicosia@qmul.ac.uk>`.
|
