Measures on the square as sparse graph limits

Abstract

We study a metric on the set of finite graphs in which two graphs are considered to be similar if they have similar bounded dimensional "factors". We show that limits of convergent graph sequences in this metric can be represented by symmetric Borel measures on $[0,1{]}^2$. This leads to a generalization of dense graph limit theory to sparse graph sequences.

31 pages, references added

References in corpus (1)

• Sparse graph limits, entropy maximization and transitive graphs