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Today two keywords more and more frequently recur over the Internet: Peer-to-Peer (P2P) and social networks. P2P, in all of its different declinations, represents a widely-adopted approach for content distribution, particularly for video diffusion. In parallel, the proliferation of social networks is an analogously stunning phenomenon, of unprecedented popularity and scope. In the present work we examine a mesh-based P2P overlay, specifically designed for video streaming, and put forth some modifications to the neighborhood creation and chunk scheduling algorithm the platform adopts, with the goal of favoring peers belonging to a social network and granting them better performance. The improvements that such modifications attain are measured in terms of delivery ratio (throughput) and playback delay. We find that it is possible to guarantee a clear service differentiation, so that social network peers experience an improved viewing experience at the expense of ordinary overlay members, and that the scheduling mechanism modifications warrant the more consistent gains, we also show the role that different percentages of peers belonging to the social network have on the considered metrics. We finally suggest that the attained differentiated service level can be leveraged as an incentive to convince peers of the video overlay to join the social network.