Phase transition in the detection of modules in sparse networks

@article{Decelle2011PhaseTI,
  title={Phase transition in the detection of modules in sparse networks},
  author={A. Decelle and F. Krzakala and C. Moore and L. Zdeborov{\'a}},
  journal={Physical review letters},
  year={2011},
  volume={107 6},
  pages={
          065701
        }
}
We present an asymptotically exact analysis of the problem of detecting communities in sparse random networks generated by stochastic block models. Using the cavity method of statistical physics and its relationship to belief propagation, we unveil a phase transition from a regime where we can infer the correct group assignments of the nodes to one where these groups are undetectable. Our approach yields an optimal inference algorithm for detecting modules, including both assortative and… Expand
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