We provide the first analysis of altruism in networks. Agents are embedded in a fixed network and care about the well‐being of their network neighbors. Depending on incomes, they may provide financial support to their poorer friends. We study the Nash equilibria of the resulting game of transfers. We show that equilibria maximize a concave potential function. We establish existence, uniqueness of equilibrium consumption, and generic uniqueness of equilibrium transfers. We characterize the geometry of the network of transfers and highlight the key role played by transfer intermediaries. We then study comparative statics. A positive income shock to an individual benefits all. For small changes in incomes, agents in a component of the network of transfers act as if they were organized in an income‐pooling community. A decrease in income inequality or expansion of the altruism network may increase consumption inequality.