# Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications

@article{Decelle2011AsymptoticAO, title={Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications}, author={Aur{\'e}lien Decelle and Florent Krzakala and Cristopher Moore and Lenka Zdeborov{\'a}}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2011}, volume={84 6 Pt 2}, pages={ 066106 } }

In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We use the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram. We describe in detail properties of the detectability-undetectability phase transition and the easy-hard phase transition for the community…

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