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# Stochastic Block Model and Community Detection in Sparse Graphs: A spectral algorithm with optimal rate of recovery

; Proceedings of The 28th Conference on Learning Theory, PMLR 40:391-423, 2015.

#### Abstract

In this paper, we present and analyze a simple and robust spectral algorithm for the stochastic block model with k blocks, for any k fixed. Our algorithm works with graphs having constant edge density, under an optimal condition on the gap between the density inside a block and the density between the blocks. As a co-product, we settle an open question posed by Abbe et. al. concerning censor block models.