Due to the rich information in graph data, the technique for privacy protection in published social networks is still in its infancy, as compared to the protection in relational databases. In this paper we identify a new type of attack called a friendship attack. In a friendship attack, an adversary utilizes the degrees of two vertices connected by an edge to re-identify related victims in a published social network data set. To protect against such attacks, we introduce the concept of k 2 -degree anonymity, which limits the probability of a vertex being re-identified to 1/k. For the k 2 -degree anonymization problem, we propose an Integer Programming formulation to find optimal solutions in small-scale networks. We also present an efficient heuristic approach for anonymizing large-scale social networks against friendship attacks. The experimental results demonstrate that the proposed approaches can preserve much of the characteristics of social networks.

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