Differentially Private Graph Publishing Through Noise-Graph Addition

Differential privacy is commonly used for graph analysis in the interactive setting, were a query of some graph statistic is answered with additional noise to avoid leaking private information. In such setting, only a statistic can be studied. However, in the non-interactive setting, the data may be protected with differential privacy and then published, allowing for all kinds of privacy preserving analyses. We present a noise-graph addition method to publish graphs with differential privacy guarantees. We show its relation to the probabilities in the randomized response matrix and prove that such probabilities can be chosen in such a way to preserve the sparseness of the original graph in the protected graph. Thus, better preserving the utility for different tasks, such as link prediction. Additionally, we show that the previous models of random perturbation and random sparsification are differentially private, and calculate the epsilon guarantees that they provide depending on their specifications.