  Scientists are increasingly interested in discovering community structure
from modern relational data arising on large-scale social networks. While many
methods have been proposed for learning community structure, few account for
the fact that these modern networks arise from processes of interactions in the
population. We introduce block edge exchangeable models (BEEM) for the study of
interaction networks with latent node-level community structure. The block
vertex components model (B-VCM) is derived as a canonical example. Several
theoretical and practical advantages over traditional vertex-centric approaches
are highlighted. In particular, BEEMs allow for sparse degree structure and
power-law degree distributions within communities. Our theoretical analysis
bounds the misspecification rate of block assignments, while supporting
simulations show the properties of the network can be recovered. A
computationally tractable Gibbs algorithm is derived. We demonstrate the
proposed model using post-comment interaction data from Talklife, a large-scale
online peer-to-peer support network, and contrast the learned communities from
those using standard algorithms including spectral clustering and
degree-correct stochastic block models.
