This paper studies network formation in settings where players are heterogeneous with respect to benefits as well as the costs of forming links. Our results demonstrate that centrality, center-sponsorship and short network diameter are robust features of equilibrium networks. We find that in a society with many groups, where it is cheaper to connect within groups as compared to across groups, strategic play by individuals leads to a network architecture in which there is a core group which is entirely internally connected while all the other groups are entirely externally linked and hence completely fragmented. Since internal/within group links are cheaper to form, this implies that individual incentives may generate a significant waste of valuable social resources.