Accessibility setting

Section: New Results

A spectral method for community detection in moderately-sparse degree-corrected stochastic block models

In the ordinary stochastic block model, all degrees in a cluster have the same expected degree. The Degree-Corrected Stochastic Block Models (DC-SBM) is a generalization of the former where the expected degrees of individual nodes follow a prescribed degree-sequence. We consider community detection in the DC-SBM in a paper currently in preparation [44] . We perform spectral clustering on a suitably normalized adjacency matrix. This leads to consistent recovery of the block-membership of all but a vanishing fraction of nodes, in the regime where the lowest degree is of order log$\left(n\right)$ or higher. The main contributions of this paper are $\left(i\right)$ the fact that recovery succeeds for very heterogeneous degree-distributions and $\left(ii\right)$ a clean analysis for the DC-SBM, which is a messy model.