Graph diffusion, which iteratively propagates real-valued substances among the graph, is used in numerous graph/network-involved applications. However, releasing diffusion vectors may reveal sensitive linking information in the data such as transaction information in financial network data. However, protecting the privacy of graph data is challenging due to its interconnected nature. This work proposes a novel graph diffusion framework with edge-level differential privacy guarantees by using noisy diffusion iterates. The algorithm injects Laplace noise per diffusion iteration and adopts a degree-based thresholding function to mitigate the high sensitivity induced by low-degree nodes. Our privacy loss analysis is based on Privacy Amplification by Iteration (PABI), which to our best knowledge, is the first effort that analyzes PABI with Laplace noise and provides relevant applications. We also introduce a novel Infinity-Wasserstein distance tracking method, which tightens the analysis of privacy leakage and makes PABI more applicable in practice. We evaluate this framework by applying it to Personalized Pagerank computation for ranking tasks. Experiments on real-world network data demonstrate the superiority of our method under stringent privacy conditions.

翻译：图扩散通过在图结构中迭代传播实值物质，被广泛应用于各类图/网络相关应用中。然而，直接发布扩散向量可能泄露数据中的敏感连接信息，例如金融网络数据中的交易记录。由于图数据固有的互联特性，保护其隐私面临巨大挑战。本研究提出一种具有边级差分隐私保证的新型图扩散框架，该框架通过使用带噪声的扩散迭代实现隐私保护。算法在每次扩散迭代中注入拉普拉斯噪声，并采用基于节点度的阈值函数以缓解低度节点引起的高敏感性问题。我们的隐私损失分析基于迭代隐私放大（PABI）理论，据我们所知，这是首次在拉普拉斯噪声背景下分析PABI并给出具体应用的研究。我们还提出了一种新颖的无穷维Wasserstein距离追踪方法，该方法能够收紧隐私泄露分析，使PABI理论更具实践适用性。我们通过将该框架应用于个性化PageRank计算中的排序任务进行评估。在真实网络数据上的实验表明，我们的方法在严格隐私约束条件下具有优越性能。