Multigraph limits and exchangeability
arXiv:0910.0547
Abstract
The theory of limits of dense graph sequences was initiated by Lovasz and Szegedy. 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. The main ingredient in the construction of the limit object is Aldous' representation theorem for exchangeable arrays.
32 pages