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

TL;DR

N2E addresses the challenge of enforcing node-level differential privacy on graph analytics by reducing node-DP tasks to edge-DP tasks. It introduces a distance-preserving clipping mechanism and a node-DP maximum-degree estimator to produce a clipping threshold $ au^*$ that tightly bounds node contributions, enabling reuse of existing edge-DP mechanisms. The framework combines these components into a three-step process that preserves node-DP guarantees while achieving error scaling with the graph’s true maximum degree $ ext{deg}(G)$, rather than a worst-case bound $\u223c \u2031N$. Empirically, N2E delivers substantial utility gains, including up to $2.5 imes$ improvements in edge counting and up to $80 imes$ improvements in degree distribution estimation, and provides the first node-DP solution for maximum-degree estimation, highlighting its practical impact for privacy-conscious graph analysis.

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.

Figures (4)

• Figure 1: An example of neighboring graphs where the distance-preserving property does not hold under node-DP.
• Figure 2: Demonstration of the distance-preserving property for our node-DP clipping mechanism.
• Figure 3: Overview of the N2E framework.
• Figure 4: Relative error (%) of N2E and baseline methods for $Q_{\mathrm{EC}}$ and $Q_{\mathrm{DD}}$ on three datasets under varying privacy budgets $\varepsilon$.

Theorems & Definitions (25)

• definition 1: Differential Privacy
• lemma 1: Post-Processing
• lemma 2: Sequential Composition
• lemma 3: Group Privacy
• definition 2: Laplace Mechanism dwork2006calibrating
• definition 3
• lemma 4: liu2024unleash
• definition 4: Down Neighborhood Optimality
• lemma 5: fang2022shifted
• lemma 6