On constrained adding friends in social networks

Abstract

Online social networks are currently experiencing a peak and they resemble real platforms of social conversion and content delivery. Indeed, they are exploited in many ways: from conducting public opinion polls about any political issue to planning big social events for a large public. To securely perform these large-scale computations, current protocols use a simple secret sharing scheme which enables users to obfuscate their inputs. However, these protocols require a minimum number of friends, i.e. the minimum degree of the social graph should be not smaller than a given threshold. Often this condition is not satisfied by all social graphs. Yet we can reuse these graphs after some structural modifications consisting in adding new friendship relations. In this paper, we provide the first definition and theoretical analysis of the "adding friends" problem. We formally describe this problem that, given a graph G and parameter c, asks for the graph satisfying the threshold c that results from G with the minimum of edge-addition operations. We present algorithms for solving this problem in centralized social networks. An experimental evaluation on real-world social graphs demonstrates that our protocols are accurate and inside the theoretical bounds. © 2013 Springer International Publishing.