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

TL;DR

This paper introduces N2E, a framework that converts node-DP graph tasks into edge-DP tasks, improving utility by reducing error and enabling the use of existing mechanisms, with applications to degree estimation and distribution.

Contribution

The paper presents the first general framework for reducing node-DP to edge-DP in graph analytics, featuring novel techniques for degree approximation and error reduction.

Findings

Achieves up to 2.5x error reduction in edge counting

Achieves up to 80x error reduction in degree distribution estimation

Matches state-of-the-art error bounds for edge counting

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.