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PrivDPR: Synthetic Graph Publishing with Deep PageRank under Differential Privacy

Sen Zhang, Haibo Hu, Qingqing Ye, Jianliang Xu

TL;DR

This work addresses privately publishing graph data under node-level differential privacy, tackling high sensitivity and privacy-budget splitting challenges common in DP deep graph models. It proposes PrivDPR, a private deep PageRank framework that learns node representations via a deep PageRank objective and enforces DP by perturbing gradients of a targeted weight, bounded through weight normalization. The key theoretical contribution shows that increasing the network depth can control gradient sensitivity, enabling effective DP with modest budgets, while guaranteeing node-level DP. Empirically, PrivDPR outperforms state-of-the-art private graph generation baselines on structural metrics and downstream tasks, and remains competitive with non-private methods even at small privacy budgets, demonstrating strong utility for real-world graph publication and analysis.

Abstract

The objective of privacy-preserving synthetic graph publishing is to safeguard individuals' privacy while retaining the utility of original data. Most existing methods focus on graph neural networks under differential privacy (DP), and yet two fundamental problems in generating synthetic graphs remain open. First, the current research often encounters high sensitivity due to the intricate relationships between nodes in a graph. Second, DP is usually achieved through advanced composition mechanisms that tend to converge prematurely when working with a small privacy budget. In this paper, inspired by the simplicity, effectiveness, and ease of analysis of PageRank, we design PrivDPR, a novel privacy-preserving deep PageRank for graph synthesis. In particular, we achieve DP by adding noise to the gradient for a specific weight during learning. Utilizing weight normalization as a bridge, we theoretically reveal that increasing the number of layers in PrivDPR can effectively mitigate the high sensitivity and privacy budget splitting. Through formal privacy analysis, we prove that the synthetic graph generated by PrivDPR satisfies node-level DP. Experiments on real-world graph datasets show that PrivDPR preserves high data utility across multiple graph structural properties.

PrivDPR: Synthetic Graph Publishing with Deep PageRank under Differential Privacy

TL;DR

This work addresses privately publishing graph data under node-level differential privacy, tackling high sensitivity and privacy-budget splitting challenges common in DP deep graph models. It proposes PrivDPR, a private deep PageRank framework that learns node representations via a deep PageRank objective and enforces DP by perturbing gradients of a targeted weight, bounded through weight normalization. The key theoretical contribution shows that increasing the network depth can control gradient sensitivity, enabling effective DP with modest budgets, while guaranteeing node-level DP. Empirically, PrivDPR outperforms state-of-the-art private graph generation baselines on structural metrics and downstream tasks, and remains competitive with non-private methods even at small privacy budgets, demonstrating strong utility for real-world graph publication and analysis.

Abstract

The objective of privacy-preserving synthetic graph publishing is to safeguard individuals' privacy while retaining the utility of original data. Most existing methods focus on graph neural networks under differential privacy (DP), and yet two fundamental problems in generating synthetic graphs remain open. First, the current research often encounters high sensitivity due to the intricate relationships between nodes in a graph. Second, DP is usually achieved through advanced composition mechanisms that tend to converge prematurely when working with a small privacy budget. In this paper, inspired by the simplicity, effectiveness, and ease of analysis of PageRank, we design PrivDPR, a novel privacy-preserving deep PageRank for graph synthesis. In particular, we achieve DP by adding noise to the gradient for a specific weight during learning. Utilizing weight normalization as a bridge, we theoretically reveal that increasing the number of layers in PrivDPR can effectively mitigate the high sensitivity and privacy budget splitting. Through formal privacy analysis, we prove that the synthetic graph generated by PrivDPR satisfies node-level DP. Experiments on real-world graph datasets show that PrivDPR preserves high data utility across multiple graph structural properties.
Paper Structure (32 sections, 10 theorems, 12 equations, 5 figures, 6 tables, 2 algorithms)

This paper contains 32 sections, 10 theorems, 12 equations, 5 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Differential Privacy
  4. PageRank
  5. Problem Definition and Existing Solutions
  6. Problem Definition
  7. Existing Solutions
  8. Our Proposal: PrivDPR
  9. Overview
  10. Deep PageRank
  11. Gradient Perturbation
  12. How to Resist High Sensitivity?
  13. How to Resist Privacy Budget Splitting?
  14. Model Optimization
  15. Privacy and Complexity Analysis
  16. ...and 17 more sections

Key Result

theorem 1

For any function $f: G\rightarrow\mathbb{R}^r$, the Gaussian mechanism is defined as $\mathcal{A}(G) = f(G) + \mathcal{N}\left(\mathcal{S}_{f}^2\sigma^2\mathbf{I}\right)$, where $\mathcal{N}\left(\mathcal{S}_{f}^2\sigma^2\mathbf{I}\right)$ represents a zero-mean Gaussian distribution with $\sigma =

Figures (5)

  • Figure 1: Framework of our proposed PrivDPR
  • Figure 2: Privacy budget on Cora
  • Figure 3: Privacy budget on Citeseer
  • Figure 4: Privacy budget on p2p
  • Figure 5: Privacy budget on Chicago

Theorems & Definitions (13)

  • Definition 1: Edge (Node)-Level DP hay2009accurate
  • Definition 2: Sensitivity dwork2006calibrating
  • theorem 1: Gaussian Mechanism dwork2006calibrating
  • theorem 2: Sequential Composition dwork2014algorithmic
  • theorem 3: Post-Processing dwork2014algorithmic
  • lemma 1
  • Definition 3: Graph Synthesis under Bounded DP
  • theorem 4
  • lemma 2
  • theorem 5
  • ...and 3 more