In this talk, we present Bayesian and frequentist versions of finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. We make use of the fact that when the block memberships are known, stochastic blockmodels are equivalent to log-linear models. The tests for the latent block model versions combine a block membership estimator with the algebraic statistics machinery for log-linear models. We describe sufficient statistics, markov bases and marginal polytopes of these models. The general testing methodology extends to any finite mixture of log-linear models on discrete data, and as such is the first application of the algebraic statistics machinery for latent-variable models.