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：层级结构是现实世界图中常见且重要的拓扑属性，体现着监督者与下属之间的关系或人类群体的组织行为特征。随着层级结构作为新的归纳偏置被引入各类任务中的图神经网络，它隐含的拓扑关联性为攻击者提升推断攻击性能提供了可乘之机，从而引发严重的隐私泄露问题。此外，现有隐私保护框架因缺乏对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显著下降。如何在满足隐私保障的同时有效利用数据的层级属性已成为亟待解决的问题。为解决该问题，我们提出基于庞加莱模型的差异化隐私保护框架PoinDP，该框架基于双曲几何实现层级感知图嵌入保护。具体而言，PoinDP首先基于双曲空间中的庞加莱模型为每个实体学习层级权重；其次设计个性化层级感知敏感度机制，用于量化层级结构的敏感程度并自适应分配隐私保护强度；此外提出双曲高斯机制，该机制将欧氏空间中的高斯机制拓展至双曲空间，实现在双曲空间度量下满足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框架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。