Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-09-14
Phys. Rev. E 84, 066106 (2011)
Physics
Condensed Matter
Statistical Mechanics
25 pages, 9 figures
Scientific paper
10.1103/PhysRevE.84.066106
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 detection problem. Our analysis translates naturally into a belief propagation algorithm for inferring the group memberships of the nodes in an optimal way, i.e., that maximizes the overlap with the underlying group memberships, and learning the underlying parameters of the block model. Finally, we apply the algorithm to two examples of real-world networks and discuss its performance.
Decelle Aurélien
Krzakala Florent
Moore Cristopher
Zdeborová Lenka
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