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Finding Statistically Significant Communities in Networks

Figure 8

Test on undirected and unweighted LFR benchmark with overlapping communities.

The parameters are: , , , , . S and B indicate the usual ranges of community sizes we use: and , respectively. We tested OSLOM against two recent methods to find covers in graphs: COPRA [52] and MOSES [54]. The left panel displays the normalized mutual information (NMI) between the planted cover and the one recovered by the algorithm, as a function of the fraction of overlapping vertices. Each overlapping vertex is shared between two clusters. The four curves correspond to different values of the mixing parameter ( and ) and to the community size ranges S and B. The right panel shows a test on graphs whose vertices are all shared between clusters. Each vertex is member of the same number of clusters. The plot shows the NMI as a function of the number of memberships of the vertices. Each curve corresponds to a given value of the average degree . The graph parameters are , , , , . Community sizes are in the range .

Figure 8