Inference and Phase Transitions in the Detection of Modules in Sparse Networks
Abstract
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 disassortative functional modules, assessing their significance, and learning the parameters of the underlying block model. Our algorithm is scalable and applicable to realworld networks, as long as they are well described by the block model.
 Publication:

Physical Review Letters
 Pub Date:
 August 2011
 DOI:
 10.1103/PhysRevLett.107.065701
 arXiv:
 arXiv:1102.1182
 Bibcode:
 2011PhRvL.107f5701D
 Keywords:

 64.60.aq;
 75.10.Hk;
 89.75.Hc;
 Networks;
 Classical spin models;
 Networks and genealogical trees;
 Condensed Matter  Statistical Mechanics;
 Computer Science  Machine Learning;
 Computer Science  Social and Information Networks;
 Physics  Physics and Society
 EPrint:
 4 pages, 4 figures