Graph limits and exchangeable random graphs

TL;DR

This paper establishes a connection between deFinetti's theorem for exchangeable arrays and the theory of graph limits, translating graph theory concepts into classical probability to deepen understanding of both areas.

Contribution

It bridges the gap between exchangeable array theory and graph limits, providing a unified probabilistic framework for graph convergence.

Findings

Unified framework for exchangeable graphs and graph limits

Translation of graph theory into classical probability

Enhanced understanding of graph convergence behavior

Abstract

We develop a clear connection between deFinetti's theorem for exchangeable arrays (work of Aldous--Hoover--Kallenberg) and the emerging area of graph limits (work of Lovasz and many coauthors). Along the way, we translate the graph theory into more classical probability.