k-Anonymization of Social Networks by Vertex Addition

With an abundance of social network data being released, the need to protect sensitive information within these networks has become an important concern of data publishers. In this paper we focus on the popular notion of kanonymization as applied to node degrees in a social network. Given such a network N , the problem we study is to transform N to N , such that the degree of each node in N ′ is attained by at least k − 1 other nodes in N . Apart from previous work, we permit modifications to the node set, rather than the edge set, and this offers unique advantages with respect to the utility of the released anonymized network. We study both vertex-labeled and unlabeled graphs, since instances of each occur in real-world social networks. Under the constraint of minimum node additions, we show that on vertex-labeled graphs, the problem is NP-complete. For unlabeled graphs, we give an efficient (near-linear) algorithm and show that it gives solutions that are optimal modulo k, a guarantee that is novel in the literature. Additionally, we demonstrate empirically that commonlystudied structural properties of the network, such as clustering coefficient, are quite minorly distorted by the anonymization procedure.