Graph limits: An alternative approach to s-graphons

Abstract

We show that s-convergence of graph sequences is equivalent to the convergence of certain compact sets, called shapes, of Borel probability measures. This result is analogous to the characterization of graphon convergence (with respect to the cut distance) by the convergence of envelopes, due to Dole\v{z}al, Greb\'{i}k, Hladk\'{y}, Rocha, and Rozho\v{v}.