Certified Signed Graph Unlearning

TL;DR

This work tackles privacy in signed graphs by developing Certified Signed Graph Unlearning (CSGU), a method that respects the heterogeneous positive/negative edges encoded by SGNNs while delivering $(\epsilon,\delta)$-differential privacy guarantees. CSGU combines a Triadic Influence Neighborhood to localize certified unlearning, sociological influence quantification (balancing balance theory and status theory) to allocate the privacy budget, and weighted parameter updates via influence functions with DP noise to minimize utility loss. Empirical results across four signed datasets and four SGNN backbones show that CSGU outperforms existing unlearning methods in both utility preservation and unlearning effectiveness, while maintaining computational efficiency. The approach offers practical privacy protections for sensitive relational data and provides a tractable framework for certified unlearning in complex signed networks.

Abstract

Signed graphs model complex relationships through positive and negative edges, with widespread real-world applications. Given the sensitive nature of such data, selective removal mechanisms have become essential for privacy protection. While graph unlearning enables the removal of specific data influences from Graph Neural Networks (GNNs), existing methods are designed for conventional GNNs and overlook the unique heterogeneous properties of signed graphs. When applied to Signed Graph Neural Networks (SGNNs), these methods lose critical sign information, degrading both model utility and unlearning effectiveness. To address these challenges, we propose Certified Signed Graph Unlearning (CSGU), which provides provable privacy guarantees while preserving the sociological principles underlying SGNNs. CSGU employs a three-stage method: (1) efficiently identifying minimal influenced neighborhoods via triangular structures, (2) applying sociological theories to quantify node importance for optimal privacy budget allocation, and (3) performing importance-weighted parameter updates to achieve certified modifications with minimal utility degradation. Extensive experiments demonstrate that CSGU outperforms existing methods, achieving superior performance in both utility preservation and unlearning effectiveness on SGNNs.

Figures (12)

• Figure 1: The limitations of directly applying existing graph unlearning methods to signed graphs.
• Figure 2: Overview of the proposed Certified Signed Graph Unlearning (CSGU). The influenced neighborhood $\mathcal{R}$ is formed after deleting a node from $\mathcal{G}$.
• Figure 3: Comparison of the unlearning efficiency (Time) between CSGU and baselines for 2.5% node unlearning on Slashdot. The results show that our method consistently achieves the lowest unlearning time across the majority of experimental settings.
• Figure 4: Comparison of the unlearning effectiveness (MI-AUC $\downarrow$) between CSGU and baselines under different ratios for edge unlearning with SDGNN backbone.
• Figure 5: Effect of the hyperparameter $\alpha$ on the trade-off between utility retention and unlearning performance for 2.5% edge unlearning on Slashdot with SiGAT. $\alpha$ balances the principles of balance and status theories.

Theorems & Definitions (30)

• Definition 1: Influence Completeness
• Theorem 1: Certification Complexity
• Definition 2: Triadic Closure
• Theorem 2: Time Complexity
• Proof 1
• Theorem 3: Space Complexity
• Proof 2
• Lemma 1: Individual Edge Sensitivity
• Proof 3
• Corollary 1: Global Sensitivity