This paper models conflict as a contest within a network of friendships and enmities. We assume that each player is either in a friendly or in an antagonistic relation with every other player and players compete for winning by exerting costly efforts. We axiomatically characterize a success function which determines the win probability of each player given the efforts and the network of relations. In an extension, we allow for varying intensities of friendships and enmities. This framework allows for the study of strategic incentives and friendship formation under conflict as well as the application of stability concepts of network theory to contests.