Hierarchy is an important and commonly observed topological property in real-world graphs that indicate the relationships between supervisors and subordinates or the organizational behavior of human groups. As hierarchy is introduced as a new inductive bias into the Graph Neural Networks (GNNs) in various tasks, it implies latent topological relations for attackers to improve their inference attack performance, leading to serious privacy leakage issues. In addition, existing privacy-preserving frameworks suffer from reduced protection ability in hierarchical propagation due to the deficiency of adaptive upper-bound estimation of the hierarchical perturbation boundary. It is of great urgency to effectively leverage the hierarchical property of data while satisfying privacy guarantees. To solve the problem, we propose the Poincar\'e Differential Privacy framework, named PoinDP, to protect the hierarchy-aware graph embedding based on hyperbolic geometry. Specifically, PoinDP first learns the hierarchy weights for each entity based on the Poincar\'e model in hyperbolic space. Then, the Personalized Hierarchy-aware Sensitivity is designed to measure the sensitivity of the hierarchical structure and adaptively allocate the privacy protection strength. Besides, the Hyperbolic Gaussian Mechanism (HGM) is proposed to extend the Gaussian mechanism in Euclidean space to hyperbolic space to realize random perturbations that satisfy differential privacy under the hyperbolic space metric. Extensive experiment results on five real-world datasets demonstrate the proposed PoinDP's advantages of effective privacy protection while maintaining good performance on the node classification task.

翻译：层级是现实世界图中常见且重要的拓扑性质，它反映了监督者与下属之间的关系或人类群体的组织行为。当层级作为新的归纳偏置引入图神经网络的各类任务时，隐含着供攻击者提升推理攻击性能的潜在拓扑关联，导致严重的隐私泄露问题。此外，现有的隐私保护框架因缺乏层级扰动边界的自适应上界估计能力，在层级传播过程中保护能力会下降。因此，亟需在满足隐私保护要求的同时有效利用数据的层级特性。为解决该问题，我们基于双曲几何提出庞加莱差分隐私框架PoinDP，用于保护具有层级感知特性的图嵌入。具体而言，PoinDP首先基于双曲空间中的庞加莱模型学习每个实体的层级权重；随后设计个性化层级感知敏感度，以量化层级结构的敏感度并自适应分配隐私保护强度。此外，我们提出双曲高斯机制，将欧氏空间中的高斯机制拓展至双曲空间，实现满足双曲空间度量下差分隐私的随机扰动。在五个真实数据集上的大量实验结果表明，所提出的PoinDP在保持节点分类任务良好性能的同时，具有有效的隐私保护优势。