Differentially Private Graph Diffusion with Applications in Personalized PageRanks

TL;DR

This paper introduces a differentially private graph diffusion method that protects sensitive link information while accurately computing personalized PageRanks, using noisy diffusion and novel privacy analysis techniques.

Contribution

It proposes a new edge-level differential privacy framework for graph diffusion with Laplace noise and introduces PABI analysis and Infinity-Wasserstein distance tracking for improved privacy guarantees.

Findings

Method outperforms existing approaches under strict privacy constraints.

Effective in real-world network data for personalized PageRank.

Provides theoretical privacy guarantees with practical evaluation.

Abstract

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.