The equivariant cohomology ring of a Hamiltonian manifold can be a rather difficult object to study. But for a particular category of manifolds, called GKM (Goresky-Kottwitz-MacPherson) spaces, the equivariant cohomology ring can be understood entirely in terms of a graph, the GKM graph. In this talk we introduce their main properties and describe how an equivariant map can be used to simplify the understanding of their cohomology rings. In particular we prove a graph theoretical version of the Serre-Leray theorem, and a generalization of the Chang-Skjelbred Theorem. As an example, we study the projection maps from complete flag varieties to partial flag varieties from this combinatorial perspective.