Networks, Communities and the Ground-Truth

About

Nodes in complex networks organize into communities of nodes that share a common property, role or function, such as social communities, functionally related proteins, or topically related webpages. Identifying such communities is crucial to the understanding of the structural and functional roles of networks.

Current work on overlapping community detection (often implicitly) assumes that community overlaps are less densely connected than non-overlapping parts of communities. This is unnatural as it means that the more communities nodes share, the less likely it is they are linked. We validate this assumption on a diverse set of large networks and find an increasing relationship between the number of shared communities of a pair of nodes and the probability of them being connected by an edge, which means that parts of the network where communities overlap tend to be more densely connected than the non-overlapping parts of communities.

Existing community detection methods fail to detect communities with such overlaps. We propose a model-based community detection method that builds on bipartite node-community affiliation networks. Our method successfully detects overlapping, non-overlapping and hierarchically nested communities. We accurately identify relevant communities in networks ranging from biological protein-protein interaction networks to social, collaboration and information networks. Our results show that while networks organize into overlapping communities, globally networks also exhibit a nested core-periphery structure, which arises as a consequence of overlapping parts of communities being more densely connected.