Community-Affiliation Graph Model for Overlapping Network Community Detection

One of the main organizing principles in real-world networks is that of network communities, where sets of nodes organize into densely linked clusters. Communities in networks often overlap as nodes can belong to multiple communities at once. Identifying such overlapping communities is crucial for the understanding the structure as well as the function of real-world networks. Even though community structure in networks has been widely studied in the past, practically all research makes an implicit assumption that overlaps between communities are less densely connected than the non-overlapping parts themselves. Here we validate this assumption on 6 large scale social, collaboration and information networks where nodes explicitly state their community memberships. By examining such ground-truth communities we find that the community overlaps are more densely connected than the non-overlapping parts, which is in sharp contrast to the conventional wisdom that community overlaps are more sparsely connected than the communities themselves. Practially all existing community detection methods fail to detect communities with dense overlaps. We propose Community-Affiliation Graph Model, a model-based community detection method that builds on bipartite node-community affiliation networks. Our method successfully captures overlapping, non-overlapping as well as hierarchically nested communities, and identifies relevant communities more accurately than the state-of-the-art methods in networks ranging from biological to social and information networks.