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Finding Statistically Significant Communities in Networks

Figure 10

Test on hierarchical LFR benchmark graphs (unweighted, undirected and without overlapping clusters).

We compare three pairs of partitions: the lowest hierarchical partition found by the algorithm (indicated by ) with the set of micro-communities of the benchmark (Fine); the lowest hierarchical partition found by the algorithm with the set of macro-communities of the benchmark (Coarse); the second lowest hierarchical partition found by the algorithm (indicated by ) with the set of macro-communities of the benchmark. The corresponding similarities are plotted as a function of , for fixed . There are vertices, the average degree , the maximum degree , the size of the macro-communities lies between and vertices, the size of the micro-communities lies between and vertices. The exponents of the degree and community size distributions are and .

Figure 10

doi: https://doi.org/10.1371/journal.pone.0018961.g010