Multigraph limits and exchangeability

The theory of limits of dense graph sequences was initiated by Lovász and Szegedy in [8]. 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 Diaconis and Janson in [5]. The main ingredient in the construction of the limit object is Aldous’ representation theorem for exchangeable arrays, see [1].