A non-cooperative model of network formation is developed. Agents form links with others based on the cost of the link and its assessed benefit. Link formation is one-sided, i.e., agents can initiate links with other agents without their consent, provided the agent forming the link makes the appropriate investment. Information flow is two-way. The model builds on the work of Bala and Goyal, but allows for agent heterogeneity. Whereas they permit links to fail with a certain common probability, in our model the probability of failure can be different for different links. We investigate Nash networks that exhibit connectedness and super-connectedness. We provide an explicit characterization of certain star networks. Efficiency and Pareto-optimality issues are discussed through examples. We explore alternative model specifications to address potential shortcomings.