Graphs are an attractive formalism because, despite over-simplification, they seem capable of representing the rich structure we see in complex dynamical systems. Mean-field style approximations can be highly effective at describing equilibrium properties. In this talk, we begin by reviewing these methods and discuss how to make systematic corrections to them via spatial expansions. Adapting these methods for dynamic systems is an ongoing project. Through two simple case studies -- the random walk and the SIS model -- we make a start on this.