1. gn(1)
  2. www.complex-networks.net
  3. gn(1)

NAME

gn - Find communities using the Girvan-Newman algorithm

SYNOPSIS

gn graph_in

DESCRIPTION

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 graphs.

PARAMETERS

graph_in
undirected input graph (edge list). If is equal to - (dash), read the edge list from STDIN.

OUTPUT

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
    ... 

where 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
    ....

where nc_i is the number of communities after the i-th edge has been removed and Q_i is the corresponding value of modularity.

EXAMPLES

We can use gn to find communities in the graph karate_club_unweighted.txt (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 file karate_gn_trace.

SEE ALSO

modularity(1), cnm(1), label_prop(1)

REFERENCES

AUTHORS

(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <v.nicosia@qmul.ac.uk>.

  1. www.complex-networks.net
  2. September 2017
  3. gn(1)