The recent discovery of topological insulators has triggered interest to the search of topological edge states of light. So far the research has been focused in classical optics domain. Topological states of quantum light promise transport and processing of quantum information, robust against the disorder. Here, we focus on the interaction-driven edge states of photon pairs in periodic arrays of nonlinear optical cavities. We link the edge state existence to the two-photon quantum walk graph connectivity, thus uncovering the topological nature of the many-body problem in complex lattices.