Differentially Private Community Detection over Stochastic Block Models with Graph Sketching

There has been significant recent progress in under-standing the fundamental limits of community detection when the graph is generated from a stochastic block model (SBM). In this paper, we study the community detection problem over binary symmetric SBMs while preserving the privacy of the individual connections between the vertices. We present and analyze the associated information-theoretic tradeoff for differentially private exact recovery of the underlying communities through deriving sufficient separation conditions between the intra-community and inter-community connection probabilities while taking into account the privacy budget and graph sketching as a speed-up technique to improve the computational complexity of maximum likelihood (ML) based recovery algorithms