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  . 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 or higher. The main contributions of this paper are the fact that recovery succeeds for very heterogeneous degree-distributions and a clean analysis for the DC-SBM, which is a messy model.