<p>This paper proposes a non-cooperative game of network formation in which creating access to the network – for oneself and others – is a public good. Link formation therefore reflects a trade-off between the social value of links and their private cost. The paper characterizes the architecture of strict Nash networks. Strict Nash equilibria are either flat or hierarchical. Flat equilibria consist of a wheel (i.e., a directed cycle) that may or may not encompass all agents. Hierarchical equilibria are trees in which some agents act as intermediaries between otherwise disconnected groups. When the cost of link formation is sufficiently low, the exhaustive wheel is the unique equilibrium architecture and best-response dynamics converge to it with probability one. For intermediate costs, multiple equilibrium architectures coexist and can be Pareto-ranked: the exhaustive wheels dominate the non-exhaustive ones and the empty network, and trees dominate the empty network.</p>