We show that if a sequence of dense graphs Gn has the property that for every fixed graph F , the density of copies of F in Gn tends to a limit, then there is a natural “limit object”, namely a… (More)

We develop a clear connection between de Finetti’s theorem for exchangeable arrays (work of Aldous–Hoover–Kallenberg) and the emerging area of graph limits (work of Lovász and many coauthors). Along… (More)

Szemerédi’s Regularity Lemma is a fundamental tool in graph theory: it has many applications to extremal graph theory, graph property testing, combinatorial number theory, etc. The goal of this paper… (More)

The motivation of this paper comes from statistical physics as well as from combinatorics and topology. The general setup in statistical mechanics can be outlined as follows. Let G be a graph and let… (More)

We define a distance of two graphs that reflects the closeness of both local and global properties. We also define convergence of a sequence of graphs, and show that a graph sequence is convergent if… (More)

In this paper we develop a measure-theoretic method to treat problems in hypergraph theory. Our central theorem is a correspondence principle between three objects: an increasing hypergraph sequence,… (More)

We show that an important recent result of Alon and Shapira on testing hereditary graph properties can be derived from the existence of a limit object for convergent graph sequences.

We investigate families of graphs and graphons (graph limits) that are determined by a finite number of prescribed subgraph densities. Our main focus is the case when the family contains only one… (More)

Let A = {a1, . . . , ak} and B = {b1, . . . , bk} be two subsets of an Abelian group G, k ≤ |G|. Snevily conjectured that, when G is of odd order, there is a permutation π ∈ Sk such that the sums ai… (More)