A critical point for random graphs with a given degree sequence
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
An Introduction to Variational Methods for Graphical Models
Machine Learning
Assessing a Mixture Model for Clustering with the Integrated Completed Likelihood
IEEE Transactions on Pattern Analysis and Machine Intelligence
An EM Algorithm for the Block Mixture Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast online graph clustering via Erdős-Rényi mixture
Pattern Recognition
An Introduction to Metabolic Networks and Their Structural Analysis
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Assessing the exceptionality of coloured motifs in networks
EURASIP Journal on Bioinformatics and Systems Biology - Special issue on network structure and biological function: Reconstruction, modelling, and statistical approaches
Structures and hyperstructures in metabolic networks
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Improved Bayesian inference for the stochastic block model with application to large networks
Computational Statistics & Data Analysis
Community detection for proximity alignment
Integrated Computer-Aided Engineering
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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.