In mechanism design, the goal is to create rules for making a decision based on the preferences of multiple parties (agents), while taking into account that agents may behave strategically. An emerging phenomenon is to run such mechanisms on a social network; for example, Facebook recently allowed its users to vote on its future terms of use. One significant complication for such mechanisms is that it may be possible for a user to participate multiple times by creating multiple identities. Prior work has investigated the design of false-name-proof mechanisms, which guarantee that there is no incentive to use additional identifiers. Arguably, this work has produced mostly negative results. In this paper, we show that it is in fact possible to create good mechanisms that are robust to false-name-manipulation, by taking the social network structure into account. The basic idea is to exclude agents that are separated from trusted nodes by small vertex cuts. We provide key results on the correctness, optimality, and computational tractability of this approach. © 2010 Springer-Verlag.