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

TL;DR

This paper introduces a simple spectral algorithm for community detection in sparse stochastic block models, achieving optimal recovery rates and resolving an open question on censored block models.

Contribution

It presents a robust spectral algorithm that works with sparse graphs and establishes optimal conditions for community recovery, including for censored block models.

Findings

Algorithm achieves optimal recovery rate in sparse graphs

Works with constant edge density under optimal gap conditions

Resolves open question on censored block models

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.