gn - Find communities using the Girvan-Newman algorithm
gn finds the communities in graph_in using the Girvan-Newman
algorithm, based on the successive removal of edges with high
betweenness. The program prints on STDOUT the partition corresponding
to the highest value of the modularity function, and reports on STDERR
the number of communities after each edge removal and the
corresponding value of modularity.
N.B.: the program recomputes the edge betweenness of the graph after
the removal of each edge, so it is not feasible to use it on large
-(dash), read the edge list from STDIN.
The program prints on STDOUT the partition corresponding to the highest value of modularity, in the format:
## nc: NUM_COMM Q_max: Q_MAX node_1 comm_1 node_2 comm_2 node_3 comm_3 ...
comm_i is the community to which
node_i belongs. The first
output line reports the number of communities
NUM_COMM and the
corresponding value of modularity
Q_MAX of the partition.
The program prints on STDERR the number of communities (connected components) after the removal of each edge, and the corresponding value of modularity, in the format:
nc_1 Q_1 nc_2 Q_2 nc_3 Q_3 ....
nc_i is the number of communities after the i-th edge has been
Q_i is the corresponding value of modularity.
We can use
gn to find communities in the graph
(Zachary Karate Club network) with the command:
$ gn karate_club_unweighted.net 2> karate_gn_trace ### nc: 4 Q_max: 0.365631 0 1 1 1 2 2 3 1 4 3 5 3 6 3 ... 30 2 31 2 32 2 33 2 $
In this run, the command has found a partition with 4 communities
corrisponding to a modularity Q=0.365631. Notice that node 0, 1, 3,
are in community 1, node 2 is in community 2, node 4,5,6, are in
community 3 and so forth. In general, different runs will provide
different partitions, since any tie in betweenness values is broke by
choosing one of the edges with equal betweenness uniformly at
random. In this example, we have chosen to save the information about
number of communities and modularity after each edge removal in the
M. Girvan and M. E. J. Newman. "Community structure in social and biological networks". P. Natl. Acad. Sci. USA 99 (2002), 7821--7826.
V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, Methods and Applications", Appendix 17, Cambridge University Press (2017)
V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, Methods and Applications", Chapter 9, Cambridge University Press (2017)
(c) Vincenzo 'KatolaZ' Nicosia 2009-2017