Abstract:
Lovasz and Szegedy in a 2004 paper define a limit for sequences of dense graphs. These limits are the structural behavior of the graph sequence in the sense that homomorphism probabilities converge. Another nice characteristic of these limits is that they can be associated to a symmetric function \(W:[0,1]^2 \to [0,1]\). We'll look at some of the properties of these limits and characteristics of the limits of certain families of graphs.