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144 lines
4.2 KiB
144 lines
4.2 KiB
f3m(1) -- Count all the 3-node subgraphs of a directed graph
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======
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## SYNOPSIS
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`f3m` <graph_in> [<num_random>]
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## DESCRIPTION
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`f3m` performs a motif analysis on <graph_in>, i.e., it counts all the
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3-node subgraphs and computes the z-score of that count with respect
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to the corresponding configuration model ensemble.
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## PARAMETERS
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* <graph_in>:
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input graph (edge list). It must be an existing file.
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* <num_random>:
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The number of random graphs to sample from the configuration model
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for the computation of the z-score of the motifs.
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## OUTPUT
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`f3m` prints on the standard output a table with 13 rows, one for each
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of the 13 possible 3-node motifs. Each line is in the format:
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motif_number count mean_rnd std_rnd z-score
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where `motif_number` is a number between 1 and 13 that identifies the
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motif (see [MOTIF NUMBERS][] below), `count` is the number of
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subgraphs ot type `motif_number` found in <graph_in>, `mean_rnd` is
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the average number of subgraphs of type `motif_number` in the
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corresponding configuration model ensemble, and `std_rnd` is the
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associated standard deviation. Finally, `z-score` is the quantity:
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(count - mean_rnd) / std_rnd
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The program also prints a progress bar on STDERR.
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## MOTIF NUMBERS
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We report below the correspondence between the 13 possible 3-node
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subgraphs and the corresponding `motif_number`. In the diagrams,
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'O--->O' indicates a single edge form the left node to the right node,
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while 'O<==>O' indicates a double (bi-directional) edge between the
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two nodes:
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(1) O<---O--->O
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(2) O--->O--->O
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(3) O<==>O--->O
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(4) O--->O<---O
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(5) O--->O--->O
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\ ^
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\_______|
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(6) O<==>O--->O
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\ ^
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\_______|
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(7) O<==>O<---O
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(8) O<==>O<==>O
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(9) O<---O<---O
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\ ^
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\_______|
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(10) O<==>O<---O
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\ ^
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\_______|
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(11) O--->O<==>O
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\ ^
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\_______|
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(12) O<==>O<==>O
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\ ^
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\_______|
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(13) O<==>O<==>O
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^\ ^/
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\\_____//
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\_____/
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## EXAMPLES
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To perform a motif analysis on the E.coli transcription regulation
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graph, using 1000 randomised networks, we run the command:
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$ f3m e_coli.net 1000
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1 4760 4400.11 137.679 +2.614
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2 162 188.78 8.022 -3.338
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3 0 0.89 3.903 -0.228
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4 226 238.32 7.657 -1.609
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5 40 6.54 2.836 +11.800
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6 0 0.01 0.077 -0.078
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7 0 0.12 0.642 -0.192
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8 0 0.00 0.032 -0.032
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9 0 0.01 0.109 -0.110
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10 0 0.00 0.000 +0.000
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11 0 0.00 0.032 -0.032
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12 0 0.00 0.000 +0.000
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13 0 0.00 0.000 +0.000
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$
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Notice that the motif `5` (the so-called "feed-forward loop") has a
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z-score equal to 11.8, meaning that it is highly overrepresented in
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the E.coli graph with respect to the corresponding configuration model
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ensemble. Conversely, the motif `2` (three-node chain) is
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underrepresented, as made evident by value of the z-score (-3.338).
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## SEE ALSO
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johnson_cycles(1)
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## REFERENCES
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* R\. Milo et al. "Network Motifs: Simple Building Blocks of Complex
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Networks". Science 298 (2002), 824-827.
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* R\. Milo et al. "Superfamilies of evolved and designed networks."
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Science 303 (2004), 1538-1542
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* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
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Methods and Applications", Chapter 8, Cambridge University Press
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(2017)
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* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
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Methods and Applications", Appendix 16, Cambridge University Press
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(2017)
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## AUTHORS
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(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 `<v.nicosia@qmul.ac.uk>`.
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