Graphon

In graph theory and statistics, a graphon (also known as a graph limit) is a symmetric measurable function ${\displaystyle W:[0,1]^{2}\to [0,1]}$, that is important in the study of dense graphs. Graphons arise both as a natural notion for the limit of a sequence of dense graphs, and as the fundamental defining objects of exchangeable random graph models. Graphons are tied to dense graphs by the following pair of observations: the random graph models defined by graphons give rise to dense graphs almost surely, and, by the regularity lemma, graphons capture the structure of arbitrary large dense graphs.