Convergent dense sequences of graphs and their limit objects called graphons were introduced by Borgs, Chayes, Lovasz, Sos, Szegedy and Vesztergombi. Many directions of study of finite graphs extend to the study of graphons, and often yield interesting, even surprising results. In this talk we discuss the automorphism group of graphons. We prove that after an appropriate “standardization” of the graphon, the automorphism group is compact. Furthermore, we characterize the orbits of the automorphism group on k-tuples of points. Among applications we study the graph algebras defined by finite rank graphons and the space of node-transitive graphons.
This is joint work with Balazs Szegedy.