We study from both a theoretical and an empirical perspective how a network of military alliances and enmities affects the intensity of a conflict. The model combines elements from network theory and from the politico-economic theory of conflict. We postulate a Tullock contest success function augmented by an externality: each group’s strength is increased by the fighting effort of its allies, and weakened by the fighting effort of its rivals. We obtain a closed form characterization of the Nash equilibrium of the fighting game, and of how the network structure affects individual and total fighting efforts. We then perform an empirical analysis using data on the Second CongoWar, a conflict that involves many groups in a complex network of informal alliances and rivalries. We es- timate the fighting externalities, and use these to infer the extent to which the conflict intensity can be reduced through (i) removing individual groups involved in the conflict; (ii) pacification policies aimed at alleviating animosity among groups.