Properties of variational estimates of a mixture model for random graphs

Mixture models for random graphs have a complex dependency structure and a likelihood which is not computable even for moderate size networks. Variational and variational Bayes techniques are useful approaches for statistical inference of such complex models but their theoretical properties are not well known. We give a result about the consistency of variational estimates of the parameters of the model and we propose variational Bayes estimates. We compare the accuracy of the two variational methods through simulation studies and show an application to a large Protein-Protein interaction network.