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The eigenvalues of stochastic blockmodel graphs
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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 F\"{u}redi and Koml\'{o}s on the fluctuation of the largest eigenvalue for Erd\H{o}s-R\'{e}nyi graphs.
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The Spectral Barycentre of a Set of Graphs with Community Structure
The barycentre graph of a graph dataset is reconstructed by pairing the mean Laplacian spectrum with Soules-basis eigenvectors aligned to communities, and for balanced stochastic block models this reconstruction is cl...
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