 In order to impose consistency (in the sense of projectivity) between random graphs of different sizes it is natural to study the sequence of adjacency matrices arising as the upper-left formula_27 sub-matrices of some infinite array of random variables; this allows us to generate formula_29 by adding a node to formula_30 and sampling the edges formula_31 for formula_32.With this perspective, random graphs are defined as random infinite symmetric arrays formula_33.Following the fundamental importance of exchangeable sequences in classical probability, it is natural to look for an analogous notion in the random graph setting.