We introduce a class of random graphs on the reals R defined by the exchangeability of their vertices. A straightforward adaptation of a result by Kallenberg yields a representation theorem: every such random graph is characterized by three (potentially random) components: a nonnegative real I in R+, an integrable function S: R+ to R+, and a symmetric measurable function W: R+^2 to [0,1] that satisfies several weak integrability conditions. We call the triple (I,S,W) a graphex, in analogy to graphons, which characterize the (dense) exchangeable graphs on N. I will present some results about the structure and consistent estimation of these random graphs.

 Joint work with Victor Veitch.