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Online video sharing and social networking are cross-pollinating rapidly in today's Internet: Online social network users are sharing more and more media contents among each other, while online video sharing sites are leveraging social connections among users to promote their videos. An intriguing development as it is, the operational challenge in previous video sharing systems persists, em i.e., the large server cost demanded for scaling of the systems. Peer-to-peer video sharing could be a rescue, only if the video viewers' mutual resource contribution has been fully incentivized and efficiently scheduled. Exploring the unique advantages of a social network based video sharing system, we advocate to utilize social reciprocities among peers with social relationships for efficient contribution incentivization and scheduling, so as to enable high-quality video streaming with low server cost. We exploit social reciprocity with two give-and-take ratios at each peer: (1) peer contribution ratio (em PCR), which evaluates the reciprocity level between a pair of social friends, and (2) system contribution ratio (em SCR), which records the give-and-take level of the user to and from the entire system. We design efficient peer-to-peer mechanisms for video streaming using the two ratios, where each user optimally decides which other users to seek relay help from and help in relaying video streams, respectively, based on combined evaluations of their social relationship and historical reciprocity levels. Our design achieves effective incentives for resource contribution, load balancing among relay peers, as well as efficient social-aware resource scheduling. We also discuss practical implementation and implement our design in a prototype social media sharing system. Our extensive evaluations based on PlanetLab experiments verify that high-quality large-scale social media sharing can be achieved with conservative server costs.