Eigenvalues of stochastic blockmodel graphs and random graphs with low-rank edge probabilities matrices

Abstract

We derive the limiting distribution for the largest eigenvalues of the adjacency matrix for a stochastic blockmodel graph when the number of vertices tends to infinity. We show that, in the limit, these eigenvalues are jointly multivariate normal with bounded covariances. Our result extends the classic result of Furedi and Komlos on the fluctuation of the largest eigenvalue for Erdos-Renyi graphs.

Publication
Sankhya A