Multigraph limits and exchangeability (Q626051)

The theory of limits of dense graph sequences was initiated by \textit{L. Lovász and B. Szegedy} [J. Comb. Theory, Ser. B 96, No.\,6, 933--957 (2006; Zbl 1113.05092)]. We give a possible generalization of this theory to multigraphs. Our proofs are based on the correspondence between dense graph limits and countable, exchangeable arrays of random variables observed by \textit{P. Diaconis and S. Janson} [Rend. Mat. Appl., VII. Ser. 28, No. ~1, 33--61 (2008; Zbl 1162.60009)]. The main ingredient in the construction of the limit object is Aldous' representation theorem for exchangeable arrays, see \textit{D. J. Aldous} [J. Multivariate Anal. 11, 581--598 (1981; Zbl 0474.60044)].