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We propose a new local, deterministic and parameter-free algorithm thatdetects fuzzy and crisp overlapping communities in a weighted network andsimultaneously reveals their hierarchy. Using a local fitness function, thealgorithm greedily expands natural communities of seeds until the whole graphis covered. The hierarchy of communities is obtained analytically bycalculating resolution levels at which communities grow rather than numericallyby testing different resolution levels. This analytic procedure is not onlymore exact than its numerical alternatives such as LFM and GCE but also muchfaster. Critical resolution levels can be identified by searching for intervalsin which large changes of the resolution do not lead to growth of communities.We tested our algorithm on benchmark graphs and on a network of 492 papers ininformation science. Combined with a specific post-processing, the algorithmgives much more precise results on LFR benchmarks with high overlap compared toother algorithms and performs very similar to GCE.

Identification of overlapping communities and their hierarchy by locally calculating community-changing resolution levels