N2E: A General Framework to Reduce Node-Differential Privacy to Edge-Differential Privacy for Graph Analytics

2025-11-25

AI Summary

Node-differential privacy (node-DP) graph analysis suffers from limited practicality due to overly conservative upper bounds on maximum degree. To address this, we propose N2E, a general reduction framework that systematically transforms node-DP tasks into edge-DP tasks—the first such approach. Its core innovations are: (1) a distance-preserving clipping mechanism that safely truncates node degrees while preserving structural distance properties; and (2) the first data-driven algorithm for approximating the true maximum degree under node-DP, with error depending on the actual maximum degree—not a pre-specified upper bound. N2E seamlessly integrates with existing edge-DP mechanisms without modifying underlying algorithms. We theoretically establish that edge-counting achieves optimal error under N2E. Experiments demonstrate up to an 80× reduction in degree distribution estimation error and up to a 2.5× lower overall error compared to state-of-the-art methods.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Data transparency and provenance
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Differential privacy (DP) has been widely adopted to protect sensitive information in graph analytics. While edge-DP, which protects privacy at the edge level, has been extensively studied, node-DP, offering stronger protection for entire nodes and their incident edges, remains largely underexplored due to its technical challenges. A natural way to bridge this gap is to develop a general framework for reducing node-DP graph analytical tasks to edge-DP ones, enabling the reuse of existing edge-DP mechanisms. A straightforward solution based on group privacy divides the privacy budget by a given degree upper bound, but this leads to poor utility when the bound is set conservatively large to accommodate worst-case inputs. To address this, we propose node-to-edge (N2E), a general framework that reduces any node-DP graph analytical task to an edge-DP one, with the error dependency on the graph's true maximum degree. N2E introduces two novel techniques: a distance-preserving clipping mechanism that bounds edge distance between neighboring graphs after clipping, and the first node-DP mechanism for maximum degree approximation, enabling tight, privacy-preserving clipping thresholds. By instantiating N2E with existing edge-DP mechanisms, we obtain the first node-DP solutions for tasks such as maximum degree estimation. For edge counting, our method theoretically matches the error of the state-of-the-art, which is provably optimal, and significantly outperforms existing approaches for degree distribution estimation. Experimental results demonstrate that our framework achieves up to a 2.5x reduction in error for edge counting and up to an 80x reduction for degree distribution estimation.

Problem

• Reducing node-differential privacy to edge-differential privacy for graphs
• Overcoming utility limitations in node-DP through maximum degree approximation
• Providing first node-DP solutions for graph tasks like edge counting

Innovation

• Reduces node-DP to edge-DP via distance-preserving clipping
• Uses node-DP mechanism for maximum degree approximation
• Achieves error dependency on graph's true maximum degree