Relational exchangeability

A relationally exchangeable structure is a random combinatorial structure whose law is invariant with respect to relabeling its relations, as opposed to its elements. Aside from exchangeable random partitions, examples include edge exchangeable random graphs and hypergraphs, path exchangeable processes, and a range of other network-like structures that arise in statistical applications. We prove a de Finetti-type structure theorem for the general class of relationally exchangeable structures.