Karrer Brian, Newman Mark. Stochastic blockmodels and community structure in networks

Physical Review E83, 016107, 21/01/2011. - 11 p.Stochastic block models have been proposed as a tool for detecting community structure in networks as well as for generating synthetic networks for use as benchmarks. Most blockmodels, however, ignore variation in vertex degree, making them unsuitable for applications to real-world.
networks, which typically display broad degree distributions that can significantly distort the results.Here we demonstrate how the generalization of block models to incorporate this missing element leads to an improved objective function for community detection in complex networks. We also propose a heuristic algorithm for community detection using this objective function or its non-degree-corrected counterpart and show that the degree-corrected version dramatically outperforms the uncorrected one in both real-world and synthetic networks.Standard stochastic block model.
Degree-corrected stochastic block model.
Empirical networks.
Generation of synthetic networks.
Performance on synthetic networks.