We introduce and analyze a general model of a population evolving over a network of selectively neutral genotypes. We show that the population's limit distribution on the neutral network is solely determined by the network topology and given by the principal eigenvector of the network's adjacency matrix. Moreover, the average number of neutral mutant neighbors per individual is given by the matrix spectral radius. This quantifies the extent to which populations evolve mutational robustness: the insensistivity of the phenotype of mutations. Since the average neutrality is independent of evolutionary parameters---such as, mutation rate, population size, and selective advantage---one can infer global statistics of neutral network topology using simple population data available from in vitro or in vivo evolution. Populations evolving on neutral networks of RNA secondary structures show excellent agreement with out theoretical predictions. <p> <p> Submitted to Proceedings of the National Academy of Science.
