Finding unique dense communities

Finding densely connected subgraphs, also called communities, in networks are of interest for many applications. In previous work, we showed an optimization method for efficiently finding subgraphs denser than the overall network [1]. This result is derived from our studies of network processes, dynamical processes that model interactions between individual agents in networks (i.e., spread of infection or cascading failures). In this paper, we prove that these subgraphs are also unique in the sense that there are no other subgraphs in the network isomorphic to these subgraphs.