Community Recovery in Graphs with Locality

Motivated by applications in domains such as social networks and computational biology, we study the problem of community recovery in graphs with locality. In this problem, pairwise noisy measurements of whether two nodes are in the same community or different communities come mainly or exclusively from nearby nodes rather than uniformly sampled between all node pairs, as in most existing models. We present two algorithms that run nearly linearly in the number of measurements and which achieve the information limits for exact recovery.