Towards identity anonymization on graphs

The proliferation of network data in various application domains has raised privacy concerns for the individuals involved. Recent studies show that simply removing the identities of the nodes before publishing the graph/social network data does not guarantee privacy. The structure of the graph itself, and in its basic form the degree of the nodes, can be revealing the identities of individuals. To address this issue, we study a specific graph-anonymization problem. We call a graph k-degree anonymous if for every node v, there exist at least k-1 other nodes in the graph with the same degree as v. This definition of anonymity prevents the re-identification of individuals by adversaries with a priori knowledge of the degree of certain nodes. We formally define the graph-anonymization problem that, given a graph G, asks for the k-degree anonymous graph that stems from G with the minimum number of graph-modification operations. We devise simple and efficient algorithms for solving this problem. Our algorithms are based on principles related to the realizability of degree sequences. We apply our methods to a large spectrum of synthetic and real datasets and demonstrate their efficiency and practical utility.