The Peer-to-Peer (P2P) architecture has been successfully used to reduce costs and increase the scalability of Internet live streaming systems. However, the effectiveness of these applications depends largely on user (peer) cooperation. In this article we use data collected from SopCast, a popular P2P live application, to show that there is high correlation between peer centrality—out-degree, out-closeness, and betweenness—in the P2P overlay graph and peer cooperation. We use this finding to propose a new regression-based model to predict peer cooperation from its past centrality. Our model takes only peer out-degrees as input, as out-degree has the strongest correlation with peer cooperation. Our evaluation shows that our model has good accuracy and does not need to be trained too often (e.g., once each 16 min). We also use our model to sketch a mechanism to detect malicious peers that report artificially inflated cooperation aiming at, for example, receiving better quality of service.