A Differentially Private Graph Estimator

We consider the problem of making graph databases such as social network structures available to researchers for knowledge discovery while providing privacy to the participating entities. We show that for a specific parametric graph model, the Kronecker graph model, one can construct an estimator of the true parameter in a way that both satisfies the rigorous requirements of differential privacy and is asymptotically efficient in the statistical sense. The estimator, which may then be published, defines a probability distribution on graphs. Sampling such a distribution yields a synthetic graph that mimics important properties of the original sensitive graph and, consequently, could be useful for knowledge discovery.