PrivDPR: Synthetic Graph Publishing with Deep PageRank under Differential Privacy

Abstract: The objective of privacy-preserving synthetic graph publishing is to safeguard individuals' privacy while retaining the utility of original data. Most existing methods focus on graph neural networks under differential privacy (DP), and yet two fundamental problems in generating synthetic graphs remain open. First, the current research often encounters high sensitivity due to the intricate relationships between nodes in a graph. Second, DP is usually achieved through advanced composition mechanisms that tend to converge prematurely when working with a small privacy budget. In this paper, inspired by the simplicity, effectiveness, and ease of analysis of PageRank, we design PrivDPR, a novel privacy-preserving deep PageRank for graph synthesis. In particular, we achieve DP by adding noise to the gradient for a specific weight during learning. Utilizing weight normalization as a bridge, we theoretically reveal that increasing the number of layers in PrivDPR can effectively mitigate the high sensitivity and privacy budget splitting. Through formal privacy analysis, we prove that the synthetic graph generated by PrivDPR satisfies node-level DP. Experiments on real-world graph datasets show that PrivDPR preserves high data utility across multiple graph structural properties.