The eigenvalues of stochastic blockmodel graphs
This extends foundational results on eigenvalue fluctuations from Erdős-Rényi graphs to more complex network models, aiding theoretical understanding in network science and statistics.
The authors derived the limiting distribution of the largest eigenvalues in stochastic blockmodel graphs as the number of vertices increases, showing they converge to a multivariate normal distribution with bounded covariances.
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 Füredi and Komlós on the fluctuation of the largest eigenvalue for Erdős-Rényi graphs.