Players allocate their budgets to links, a local public good, and a private good. A player links in order to free ride on public good provided by others. We derive sufficient conditions for the existence of a Nash equilibrium, in which large contributors link to each other, while others link to them. If linking costs are sufficiently high, poorer players may contribute more and have more central positions in the network than richer ones do. In large societies, free riding reduces inequality only in networks in which it is initially low. Otherwise, richer players free ride more, as they can afford more links. Finally, we derive the policy implications for income redistribution.