Graphon

Summary

A graphon is a symmetric measurable function $W \colon [0, 1]^2 \to [0, 1]$. Graphons are the limit objects of sequences of dense graphs. A sequence converges when the density of each fixed small graph in it converges, and then the limit is a graphon. They also give the most general exchangeable model of a random graph. Graphons turn questions of extremal graph theory, such as Sidorenko's conjecture, into questions of analysis.