Edge exchangeable models for network data

Understand

Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets.

• Out of this mathematical impossibility emerges the question of how network data can be modeled in a way that reflects known empirical behaviors and respects basic statistical principles.
• We address this question by observing that edges, not vertices, act as the statistical units in networks constructed from interaction data, making a theory of edge-labeled networks more natural for many applications.
• In this context we introduce the concept of {\em edge exchangeability}, which unlike its vertex exchangeable counterpart admits models for networks with sparse and/or power law structure.