Community-Preserving Social Graph Release with Node Differential Privacy

The goal of privacy-preserving social graph release is to protect individual privacy while preserving data utility. Community structure, which is an important global pattern of nodes, is a crucial data utility as it is fundamental to many graph analysis tasks. Yet, most existing methods with differential privacy (DP) commonly fall into edge-DP to sacrifice security in exchange for utility. Moreover, they reconstruct graphs from the local feature-extraction of nodes, resulting in poor community preservation. Motivated by this, we develop PrivCom, a strict node-DP graph release algorithm to maximize the utility on the community structure while maintaining a higher level of privacy. In this algorithm, to reduce the huge sensitivity, we devise a Katz index based private graph feature extraction method, which can capture global graph structure features while greatly reducing the global sensitivity via a sensitivity regulation strategy. Yet, under the condition that the sensitivity is fixed, the feature captured by the Katz index, which is presented in matrix form, requires privacy budget splits. As a result, plenty of noise is injected, mitigating global structural utility. To bridge this gap, we design a private eigenvector estimation method, which yields noisy eigenvectors from extracted low-dimensional vectors. Then, a dynamic privacy budget allocation method with provable utility guarantees is developed to preserve the inherent relationship between eigenvalues and eigenvectors, so that the utility of the generated noise Katz matrix is well maintained. Finally, we reconstruct the synthetic graph via calculating its Laplacian with the noisy Katz matrix. Experimental results confirm our theoretical findings and the efficacy of PrivCom.