VEC-SBM: Optimal Community Detection with Vectorial Edges Covariates

Social networks are often associated with rich side information, such as texts and images. While numerous methods have been developed to identify communities from pairwise interactions, they usually ignore such side information. In this work, we study an extension of the Stochastic Block Model (SBM), a widely used statistical framework for community detection, that integrates vectorial edges covariates: the Vectorial Edges Covariates Stochastic Block Model (VEC-SBM). We propose a novel algorithm based on iterative refinement techniques and show that it optimally recovers the latent communities under the VEC-SBM. Furthermore, we rigorously assess the added value of leveraging edge's side information in the community detection process. We complement our theoretical results with numerical experiments on synthetic and semi-synthetic data.