Public goods are commodities that are non-rival, in that their consumption by one user does not reduce its availability to others. Examples include security, clean air, and information and innovation. In this talk, we consider a network of users who make private contributions towards the provision of a public good, and study how the network structure affects the outcomes of these users' strategic interactions. We identify necessary and sufficient conditions for the uniqueness of the Nash equilibria of these games, extending several existing results in the literature. We further show that a user's action in the Nash equilibria or Pareto efficient outcomes of these games can be determined by the user's (alpha-)centrality in the interaction network.