On Exchangeability in Network Models

TL;DR

This paper presents new representation theorems for exchangeable graph distributions, clarifying differences between finite and infinite exchangeability in network models using elementary geometric and graph-theoretic methods.

Contribution

It introduces novel elementary proofs for exchangeability representation theorems, highlighting key distinctions between finite and infinite graph models.

Findings

Representation theorems for exchangeable graph distributions derived

Differences between finite and infinite exchangeability clarified

Implications for statistical network modeling discussed

Abstract

We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their implications, between statistical network models that are finitely exchangeable and models that define a consistent sequence of probability distributions on graphs of increasing size.