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Random graph mixture models are now very popular for modeling real datanetworks. In these setups, parameter estimation procedures usually rely onvariational approximations, either combined with the expectation-maximisation(\textsc{em}) algorithm or with Bayesian approaches. Despite good results onsynthetic data, the validity of the variational approximation is however notestablished. Moreover, the behavior of the maximum likelihood or of the maximuma posteriori estimators approximated by these procedures is not known in thesemodels, due to the dependency structure on the variables. In this work, we showthat in many different affiliation contexts (for binary or weighted graphs),estimators based either on moment equations or on the maximization of somecomposite likelihood are strongly consistent and $\sqrt{n}$-convergent, where$n$ is the number of nodes. As a consequence, our result establishes that theoverall structure of an affiliation model can be caught by the description ofthe network in terms of its number of triads (order 3 structures) and edges(order 2 structures). We illustrate the efficiency of our method on simulateddata and compare its performances with other existing procedures. A data set ofcross-citations among economics journals is also analyzed.

New consistent and asymptotically normal estimators for random graph mixture models