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The Stochastic Block Model (Holland et al., 1983) is a mixture model forheterogeneous network data. Unlike the usual statistical framework, new nodesgive additional information about the previous ones in this model. Thereby thedistribution of the degrees concentrates in points conditionally on the nodeclass. We show under a mild assumption that classification, estimation andmodel selection can actually be achieved with no more than the empirical degreedata. We provide an algorithm able to process very large networks andconsistent estimators based on it. In particular, we prove a bound of theprobability of misclassification of at least one node, including when thenumber of classes grows.

Classification and estimation in the Stochastic Block Model based on the empirical degrees