Differentially Private Graphical Degree Sequences and Synthetic Graphs

We present an algorithm for releasing graphical degree sequences of simple undirected graphs under the framework of differential privacy. The algorithm is designed to provide utility for statistical inference in random graph models whose sufficient statistics are functions of degree sequences. Specifically, we focus on the tasks of existence of maximum likelihood estimates, parameter estimation and goodness-of-fit testing for the beta model of random graphs. We show the usefulness of our algorithm by evaluating it empirically on simulated and real-life datasets. As the released degree sequence is graphical, our algorithm can also be used to release synthetic graphs under the beta model.

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