Perfect clustering for stochastic blockmodel graphs via adjacency spectral embedding

Abstract

Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In this paper, we provide a short proof that the adjacency spectral embedding can be used to obtain perfect clustering for the stochastic blockmodel and the degree-corrected stochastic blockmodel. We also show an analogous result for the more general random dot product graph model.