Cut distance identifying graphon parameters over weak* limits

Markov Random Fields, Homomorphism Counting, and Sidorenko’s Conjecture

“…It has been shown that weakly norming graphs satisfy Sidorenko's conjecture, i.e., for a weakly norming graph G, hom(G, M H ) ≥ hom S (G, M H ) [7]. Further, it has been shown that a graph G is weakly norming if and only if hom(G, •) is convex on the set of so-called signed graphons [24], [25], a continuous extension of the discrete problem considered herein. An interesting question, then, in our context is whether or not convexity of hom(G, •), or more generally quasiconvexity, implies anything about its relationship to hom B .…”