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In P2P networks, the service availability is badly affected by the rationality of peers. However, the actual networks don't take the issue of free-riders and malicious peers, namely the rationality, as the inherent part of the topology design. Additionally, the mechanism of a peer randomly joining and leaving a network arouses the mismatching between the overlay and the underlying physical topology. This mismatching brings about a majority of P2P traffic. A Trust-aware Adaptive P2P Overlay Topology Based on Superpeer-partition is proposed to ease above problems. Peers will no longer blindly choose neighbors, but according to trust value and physical-position. Theoretic analysis and simulation show the resulting topology is more efficient than normal topology. This topology construction can effectively suppress the deceptive and fake services, improve the reliability and security, and decrease about 26 percent of the communication cost.