We consider inhomogeneous Erdős–Rényi graphs. We suppose that the maximal mean degree d satisfies d ≪ logn. We characterise the asymptotic behaviour of the n1–o(1) largest eigenvalues of the adjacency ...

We consider community detection in degree-corrected stochastic block models. We propose a spectral clustering algorithm based on a suitably normalized adjacency matrix. We show that this algorithm ...