 If these graphs converge (according to some suitable definition of convergence), then we expect the limit of these graphs to correspond to the limit of these associated functions.This motivates the definition of a graphon (short for "graph function") as a symmetric measurable function formula_2 which
captures the notion of a limit of a sequence of graphs.It turns out that for sequences of dense graphs, several apparently distinct notions of convergence are equivalent and under all of them the natural limit object is a graphon.