  Social applications mine user social graphs to improve performance in search,
provide recommendations, allow resource sharing and increase data privacy. When
such applications are implemented on a peer-to-peer (P2P) architecture, the
social graph is distributed on the P2P system: the traversal of the social
graph translates into a socially-informed routing in the peer-to-peer layer. In
this work we introduce the model of a projection graph that is the result of
decentralizing a social graph onto a peer-to-peer network. We focus on three
social network metrics: degree, node betweenness and edge betweenness
centrality and analytically formulate the relation between metrics in the
social graph and in the projection graph. Through experimental evaluation on
real networks, we demonstrate that when mapping user communities of sizes up to
50-150 users on each peer, the association between the properties of the social
graph and the projection graph is high, and thus the properties of the
(dynamic) projection graph can be inferred from the properties of the (slower
changing) social graph. Furthermore, we demonstrate with two application
scenarios on large-scale social networks the usability of the projection graph
in designing social search applications and unstructured P2P overlays.
