Statistics and Computing

, Volume 18, Issue 2, pp 173–183 | Cite as

A mixture model for random graphs

  • J.-J. Daudin
  • F. Picard
  • S. RobinEmail author


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.


Random graphs Mixture models Variational method 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Mathématiques et Informatique AppliquéesAgroParisTech and INRA UMR518ParisFrance

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