Edge Anonymity in Social Network Graphs

Edges in social network graphs may represent sensitive relationships. In this paper, we consider the problem of edges anonymity in graphs. We propose a probabilistic notion of edge anonymity, called graph confidence, which is general enough to capture the privacy breach made by an adversary who can pinpoint target persons in a graph partition based on any given set of topological features of vertexes. We consider a special type of edge anonymity problem which uses vertex degree to partition a graph. We analyze edge disclosure in real-world social networks and show that although some graphs can preserve vertex anonymity, they may still not preserve edge anonymity. We present three heuristic algorithms that protect edge anonymity using edge swap or edge deletion. Our experimental results, based on three real-world social networks and several utility measures, show that these algorithms can effectively preserve edge anonymity yet obtain anonymous graphs of acceptable utility.