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A class of random graph models is considered, combining features ofexponential-family models and latent structure models, with the goal ofretaining the strengths of both of them while reducing the weaknesses of eachof them. An open problem is how to estimate such models from large networks. Anovel approach to large-scale estimation is proposed, taking advantage of thelocal structure of such models for the purpose of local computing. The mainidea is that random graphs with local dependence can be decomposed intosubgraphs, which enables parallel computing on subgraphs and suggests atwo-step estimation approach. The first step estimates the local structureunderlying random graphs. The second step estimates parameters given theestimated local structure of random graphs. Both steps can be implemented inparallel, which enables large-scale estimation. The advantages of the two-stepestimation approach are demonstrated by simulation studies with up to 10,000nodes and an application to a large Amazon product recommendation network withmore than 10,000 products.

Large-scale estimation of random graph models with local dependence