Sequential Community Detection in High-Dimensional Temporal Graphs

Robert P. Malinas, Dogyoon Song, Alfred O. Hero III

Abstract: We propose a spectral method for sequential community detection in high-dimensional, heterogeneous temporal random graphs based on the largest eigenvalue of an entrywise shifted-and-rescaled adjacency matrix. The transformed adjacency matrix is designed to preserve spectral information about community structure in the presence of degree heterogeneity within communities: it is completely random when no communities are present (null case), but is a low-rank perturbation of a random matrix when the graph has community structure (alternative case). The largest eigenvalues of the transformed adjacency matrix are governed by the BBP phase transition from random matrix theory, and exhibit different distributions in the null (no community structure) and alternative (community structure) cases. The primary contribution of this paper is to illustrate that the BBP phase transition can be exploited in a principled method for sequential community detection in high-dimensional temporal graphs using the statistical framework of quickest change detection.