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

TL;DR

This paper introduces block edge exchangeable models (BEEM) for detecting node-level communities in interaction networks, effectively capturing sparse and power-law degree distributions, with theoretical guarantees and practical validation on social network data.

Contribution

The paper proposes BEEM, a novel class of models for community detection in interaction networks that accounts for realistic degree distributions and provides theoretical and computational tools.

Findings

BEEM accurately recovers community structure in simulated data.

Applied to Talklife data, BEEM reveals meaningful communities distinct from standard methods.

Theoretical bounds support the robustness of block assignment recovery.

Abstract

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.