We investigate the effect that population structure has upon the course of artificial evolution. We represent an arbitrary population structure by embedding a population of individuals in a graph. Each individual resides at a vertex of the graph and can only choose a mating partner from among its neighbors in the graph. Each individual mates with the selected partner and is replaced by the resultant offspring in the next generation. We embed populations in a variety of trees and mesh-structured graphs and observe differences in rates of change of average fitness and percent polymorphism over successive generations. Results indicate that populations embedded in sparse random graphs having relatively low diameter yield results similar to those embedded in complete graphs.