Graph Structure Learning with Privacy Guarantees for Open Graph Data

Publishing open graph data while preserving individual privacy remains challenging when data publishers and data users are distinct entities. Although differential privacy (DP) provides rigorous guarantees, most existing approaches enforce privacy during model training rather than at the data publishing stage. This limits the applicability to open-data scenarios. We propose a privacy-preserving graph structure learning framework that integrates Gaussian Differential Privacy (GDP) directly into the data release process. Our mechanism injects structured Gaussian noise into raw data prior to publication and provides formal $\mu$-GDP guarantees, leading to tight $(\varepsilon, \delta)$-differential privacy bounds. Despite the distortion introduced by privatization, we prove that the original sparse inverse covariance structure can be recovered through an unbiased penalized likelihood formulation. We further extend the framework to discrete data using discrete Gaussian noise while preserving privacy guarantees. Extensive experiments on synthetic and real-world datasets demonstrate strong privacy-utility trade-offs, maintaining high graph recovery accuracy under rigorous privacy budgets. Our results establish a formal connection between differential privacy theory and privacy-preserving data publishing for graphical models.