{The Erdos-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-word networks. The vertices of these networks are often structured in \textit{prior} unknown clusters (functionally related proteins or social communities) with different connectivity properties. We define a generalization of the Erdos-Rényi model called ERMG for Erdos-Rényi Mixtures for Graphs. This new model is based on mixture distributions. We give some of its properties, an algorithm to estimate its parameters and apply this method to uncover the modular structure of a network of enzymatic reactions.