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Scientists are increasingly interested in discovering community structurefrom modern relational data arising on large-scale social networks. While manymethods have been proposed for learning community structure, few account forthe fact that these modern networks arise from processes of interactions in thepopulation. We introduce block edge exchangeable models (BEEM) for the study ofinteraction networks with latent node-level community structure. The blockvertex components model (B-VCM) is derived as a canonical example. Severaltheoretical and practical advantages over traditional vertex-centric approachesare highlighted. In particular, BEEMs allow for sparse degree structure andpower-law degree distributions within communities. Our theoretical analysisbounds the misspecification rate of block assignments, while supportingsimulations show the properties of the network can be recovered. Acomputationally tractable Gibbs algorithm is derived. We demonstrate theproposed model using post-comment interaction data from Talklife, a large-scaleonline peer-to-peer support network, and contrast the learned communities fromthose using standard algorithms including spectral clustering anddegree-correct stochastic block models.

Node-level community detection within edge exchangeable models for interaction processes