Considering the fact that P2P (Peer-to-Peer) systems are self-organized and autonomous, social-control mechanism (like trust and reputation) is essential to evaluate the trustworthiness of participating peers and to combat the selfish, dishonest and malicious peer behaviors. So, naturally, we advocate that P2P systems that gradually act as an important information infrastructure should be multi-disciplinary research topic, and reflect certain features of our society. So, from economic and social perspective, this paper designs the incentive-compatible reputation feedback scheme based on well-known economic model, and characterizes the social features of trust network in terms of efficiency and cost. Specifically, our framework has two distinctive purposes: first, from high-level perspective, we argue trust system is a special kind of social network, and an accurate characterization of the structural properties of the network can be of fundamental importance to understand the dynamics of the system. Thus, inspired by the concept of weighted small-world, this paper proposes new measurements to characterize the social properties of trust system, that is, highg lobal and local efficiency, and low cost; then, from relative low-level perspective, we argue that reputation feedback is a special kind of information, and it is not free. So, based on economic model, VCG (Vickrey-Clarke-Grove)-like reputation remuneration mechanism is proposed to stimulate rational peers not only to provide reputation feedback, but truthfully offer feedback. Furthermore, considering that trust and reputation is subjective, we classify the trust into functional trust and referral trust, and extend the referral trust to include two factors: similarity and truthfulness, which can efficiently reduce the trust inference error. The preliminary simulation results show the benefits of our proposal and the emergence of certain social properties in trust network.