We provide the first analysis of altruism in networks. Agents are connected through a fixed, weighted network and care about the well-being of their network neighbors. Given some initial distribution of incomes, agents may provide financial support to their poorer friends. We characterize the Nash equilibria of this transfer game for general networks and utility functions. We show that equilibria solve a well-behaved maximization program, related to classical problems of optimal transportation on networks. We build on this reformulation and establish existence, uniqueness in consumptions and generic uniqueness in transfers. We show that transfers are affected by the geometry of the altruistic network. They flow through shortest paths and chains of transfers emerge when the network is not transitive. We analyze the effects of changes in incomes and in the network. When an agent suffers a negative income shock, the equilibrium consumption of every agent decreases weakly. We characterize the impact of small redistributions and show that decreasing income inequality may increase consumption inequality. We also characterize the impact of a small increase in altruism. While altruistic networks reduce inequality, more altruism may lead to more inequality. Joint with Eduardo Perez-Richet.