  Network data often arises via a series of structured interactions among a
population of constituent elements. E-mail exchanges, for example, have a
single sender followed by potentially multiple receivers. Scientific articles,
on the other hand, may have multiple subject areas and multiple authors. We
introduce hierarchical edge exchangeable models for the study of these
structured interaction networks. In particular, we introduce the hierarchical
vertex components model as a canonical example, which partially pools
information via a latent, shared population-level distribution. Theoretical
analysis and supporting simulations provide clear model interpretation, and
establish global sparsity and power-law degree distribution. A computationally
tractable Gibbs algorithm is derived. We demonstrate the model on both the
Enron e-mail dataset and an ArXiv dataset, showing goodness of fit of the model
via posterior predictive validation.
