Abstract

Abstract—Social applications implemented on a peer-to-peer (P2P) architecture mine the social graph of their users for improved performance in search, recommendations, resource sharing and others. In such applications, the social graph that connects their users is distributed on the peer-to-peer system: the traversal of the social graph translates to 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 mapping a social graph onto a peer-to-peer network. We analytically formulate the relation between metrics in the social graph and in the projection graph. We focus on three such graph metrics: degree centrality, node betweenness central-ity, and edge betweenness centrality. We evaluate experimentally the feasibility of estimating these metrics in the projection graph from the metrics of the social graph. Our experiments on real networks show that when mapping communities of 50-150 users on a peer, there is an optimal organization of the projection graph with respect to degree and node betweenness centrality. In this range, the association between the properties of the social graph and the projection graph is the highest, and thus the properties of the (dynamic) projection graph can be inferred from the properties of the (slower changing) social graph. We discuss the applicability of our findings to aspects of peer-to-peer systems such as data dissemination, social search, peer vulnerability, and data placement and caching. I.