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
.