Scientific questions about networks are often comparative: we want to know whether the difference between two networks is just noise, and, if not, how their structures differ. I'll describe a general framework for network comparison, based on testing whether the distance between models estimated from separate networks exceeds what we'd expect based on a pooled estimate. This framework is especially powerful with nonparametric network models, such as densities of latent node locations, or continuous generalizations of block models ("graphons"); the estimation methods for those models also let us do generate surrogate data, predict links, and summarize structure.
(Joint work with Dena Asta, Brian Karrer, and Lawrence Wang.)