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Agglomerative clustering is a well established strategy for identifyingcommunities in networks. Communities are successively merged into largercommunities, coarsening a network of actors into a more manageable network ofcommunities. The order in which merges should occur is not in general clear,necessitating heuristics for selecting pairs of communities to merge. Wedescribe a hierarchical clustering algorithm based on a local optimalityproperty. For each edge in the network, we associate the modularity change formerging the communities it links. For each community vertex, we call thepreferred edge that edge for which the modularity change is maximal. When anedge is preferred by both vertices that it links, it appears to be the optimalchoice from the local viewpoint. We use the locally optimal edges to define thealgorithm: simultaneously merge all pairs of communities that are connected bylocally optimal edges that would increase the modularity, redetermining thelocally optimal edges after each step and continuing so long as the modularitycan be further increased. We apply the algorithm to model and empiricalnetworks, demonstrating that it can efficiently produce high-quality communitysolutions. We relate the performance and implementation details to thestructure of the resulting community hierarchies. We additionally consider acomplementary local clustering algorithm, describing how to identifyoverlapping communities based on the local optimality condition.

Detecting hierarchical and overlapping network communities using locally optimal modularity changes