This paper links the two nascent economic literatures on social networks and cultural assimilation by investigating the evolution of population attributes in a simple model where agents are influenced by their acquaintances. The main conclusion of the analysis is that attributes converge to a melting-pot equilibrium, where everyone is identical, provided the social network exhibits a sufficient degree of interconnectedness. When the model is extended to allow an expanding acquaintance set, convergence is guaranteed provided a weaker interconnectedness condition is satisfied, and convergence is rapid. If the intensity of interactions with acquaintances becomes endogenous, convergence (when it occurs) is slowed when agents prefer to interact with people like themselves and hastened when interaction with dissimilar agents is preferred.