We develop a model in which connections between individuals serve as social collateral to enforce informal insurance payments. We show that: (i) The degree of insurance is governed by the expansiveness of the network, measured with the per capita number of connections that groups have with the rest of the community. "Two-dimensional" networks?like real-world networks in Peruvian villages?are sufficiently expansive to allow very good risk-sharing. (ii) In second- best arrangements, insurance is local: agents fully share shocks within, but imperfectly between endogenously emerging risk-sharing groups. We also discuss how endogenous social collateral affects our results.