  Directed graphs occur throughout statistical modeling of networks, and
exchangeability is a natural assumption when the ordering of vertices does not
matter. There is a deep structural theory for exchangeable undirected graphs,
which extends to the directed case via measurable objects known as digraphons.
Using digraphons, we first show how to construct models for exchangeable
directed graphs, including special cases such as tournaments, linear orderings,
directed acyclic graphs, and partial orderings. We then show how to construct
priors on digraphons via the infinite relational digraphon model (di-IRM), a
new Bayesian nonparametric block model for exchangeable directed graphs, and
demonstrate inference on synthetic data.
