Publishing Graphs Under Node Differential Privacy

Differential privacy (DP) has become the de facto standard of privacy protection. For graphs, there are two widely used definitions of differential privacy, namely, edge differential privacy (edge-DP) and node differential privacy (node-DP), and node-DP is preferred when the minimal unit of interest is a node. To preserve node-DP, one can develop different methods to answer each specific graph query, or develop a graph publishing method to answer all graph queries. However, no existing works worked on such graph publishing methods. In this work, we propose two methods for publishing graphs under node-DP. One is the node-level perturbation algorithm which modifies the input graph by randomly inserting and removing nodes. The other one is the edge-level perturbation algorithm which randomly removing edges and inserting nodes. Both methods can achieve a flexible privacy guarantee by adjusting the running parameters. We conduct extensive experiments on both real-world and synthetic graphs to show the effectiveness and efficiency of proposed algorithms.