  We propose a nonparametric framework for the analysis of networks, based on a
natural limit object termed a graphon. We prove consistency of graphon
estimation under general conditions, giving rates which include the important
practical setting of sparse networks. Our results cover dense and sparse
stochastic blockmodels with a growing number of classes, under model
misspecification. We use profile likelihood methods, and connect our results to
approximation theory, nonparametric function estimation, and the theory of
graph limits.
