  We consider community detection in Degree-Corrected Stochastic Block Models
(DC-SBM). We propose a spectral clustering algorithm based on a suitably
normalized adjacency matrix. We show that this algorithm consistently recovers
the block-membership of all but a vanishing fraction of nodes, in the regime
where the lowest degree is of order log$(n)$ or higher. Recovery succeeds even
for very heterogeneous degree-distributions. The used algorithm does not rely
on parameters as input. In particular, it does not need to know the number of
communities.
