On the Optimal Error Rate of Stochastic Block Model with Symmetric Side Information

Side information improves the accuracy in community detection problems. While experimental results demonstrate the superior performance of many detection methods based on both the node attributes and graph structure, the question of the fundamental limit of the error rate for exact recovery remains open. In this paper, we obtain the asymptotic optimal error rate in the sense of exact recovery for a special two-community symmetric stochastic block model (SSBM) with side information consisting of multiple features. Our result provides insight on the number of features and nodes in the graph needed for community detection.