High-throughput screens have begun to reveal the protein interaction network that underpins most cellular functions in the yeast Saccharomyces cerevisiae. How the organization of this network affects the evolution of the proteins that compose it is a fundamental question in molecular evolution. We show that the connectivity of well-conserved proteins in the network is negatively correlated with their rate of evolution. Proteins with more interactors evolve more slowly not because they are more important to the organism, but because a greater proportion of the protein is directly involved in its function. At sites important for interaction between proteins, evolutionary changes may occur largely by coevolution, in which substitutions in one protein result in selection pressure for reciprocal changes in interacting partners. We confirm one predicted outcome of this process-namely, that interacting proteins evolve at similar rates.