A translation of the pi-calculus into the MONSTR graph rewriting language is described and proved correct. The translation illustrates the heavy cost in practice of faithfully implementing the communication primitive of the pi-calculus and similar process calculi. It also illustrates the convenience of representing an evolving network of communicating agents directly within a graph manipulation formalism, both because the necessity to use delicate notions of bound variables and of scopes is avoided, and also because the standard model of graphs in set theory automatically yields a useful semantics for the process calculus. The correctness proof illustrates many features typically encountered in reasoning about graph rewriting systems, and particularly how serialisation techniques can be used to reorder an arbitrary execution into one having stated desirable properties.