The lack of cooperation in Peer-to-Peer (P2P) applications poses serious challenges to the quality of service provided to their clients, specifically in P2P live streaming applications given their strict real-time constraints. We here investigate the potential of exploiting topological properties of the P2P overlay network to predict the level of cooperation of a peer, measured by the ratio of the upload to the download traffic during a pre-defined time window. Using data collected from SopCast, we first show that centrality metrics provide good evidence of a peer’s cooperation level in the system. We then develop a regression-based model that is able to estimate, with reasonable accuracy, the level of cooperation of a peer in the near future given its centrality measures in the recent past. Our proposed strategy complements existing incentive mechanisms for cooperation in P2P live streaming, and can be applied to detect non-cooperative peers.