Article

Statistics and Computing

, Volume 18, Issue 2, pp 173-183

A mixture model for random graphs

  • J.-J. DaudinAffiliated withMathématiques et Informatique Appliquées, AgroParisTech and INRA UMR518
  • , F. PicardAffiliated withMathématiques et Informatique Appliquées, AgroParisTech and INRA UMR518
  • , S. RobinAffiliated withMathématiques et Informatique Appliquées, AgroParisTech and INRA UMR518 Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

The Erdös–Rényi model of a network is simple and possesses many explicit expressions for average and asymptotic properties, but it does not fit well to real-world networks. The vertices of those networks are often structured in unknown classes (functionally related proteins or social communities) with different connectivity properties. The stochastic block structures model was proposed for this purpose in the context of social sciences, using a Bayesian approach. We consider the same model in a frequentest statistical framework. We give the degree distribution and the clustering coefficient associated with this model, a variational method to estimate its parameters and a model selection criterion to select the number of classes. This estimation procedure allows us to deal with large networks containing thousands of vertices. The method is used to uncover the modular structure of a network of enzymatic reactions.

Keywords

Random graphs Mixture models Variational method