On the anonymizability of graphs

Many applications such as social networks, recommendation systems, email communication patterns, and other collaborative applications are built on top of graph infrastructures. The data stored on such networks may contain personal information about individuals and may therefore be sensitive from a privacy point of view. Therefore, a natural solution is to remove identifying information from the nodes and perturb the graph structure, so that re-identification becomes difficult. Typical graphs encountered in real applications are sparse. In this paper, we will show that sparse graphs have certain theoretical properties which make them susceptible to re-identification attacks. We design a systematic way to exploit these theoretical properties in order to construct re-identification signatures, which are also known as characteristic vectors. These signatures have the property that they are extremely robust to perturbations, especially for sparse graphs. We use these signatures in order to create an effective attack algorithm. We supplement our theoretical results with experimental tests using a number of algorithms on real data sets. These results confirm that even low levels of anonymization require perturbation levels which are significant enough to result in a massive loss of utility. Our experimental results also show that the true anonymization level of graphs is much lower than is implied by measures such as \(k\)-anonymity. Thus, the results of this paper establish that the problem of graph anonymization has fundamental theoretical barriers which prevent a fully effective solution.