Abstract: Community detection refers to the problem of clustering the nodes of a network (either a graph or a hypergrah) into groups. Various algorithms are available for community detection, all of which apply to uncensored networks. In practice, a network may have censored (or missing) values, which have been shown to have a non-negligible effect on the structural properties of a network. In this study, we examine community detection in a censored m-uniform hypergraph from an information-theoretic point of view. As such, we derive the information-theoretic threshold for the exact recovery of the community structure. Furthermore, we propose a polynomial-time algorithm to exactly recover the community structure up to the threshold. The proposed algorithm consists of a spectral algorithm plus a refinement step. It is also interesting to determine whether a single spectral algorithm without refinement achieves the threshold. To this end, we explore the semi-definite relaxation algorithm and analyze its performance.

Key words and phrases: Censored hypergraph, community detection, exact recovery, information-theoretic threshold.