PriDyG: Privacy-preserving Dynamic Graph Inference with LLM-GNN Collaboration

Graph Neural Networks (GNNs) have shown considerable success in learning from graph-structured data, but their use in privacy-sensitive areas remains difficult because graph structure can leak sensitive link information. To satisfy edge-level differential privacy, a common approach is to inject noise into all elements of the graph's adjacency matrix, thereby obfuscating the existence of any single edge. However, stronger privacy requires more noise, and excessive noise reduces utility, making the privacy-utility balance a major barrier to practical privacy-preserving graph learning. To address this issue, we propose EdgeRefine, a local differential privacy framework that improves this trade-off through adaptive edge refinement. EdgeRefine first estimates edge-existence probabilities using Jaccard similarity and ranks edges for noisy edge removal. To ensure the sparsity and reliability of the final graph, it uses the privacy budget $ε$ to determine the ratio of true to false edges, samples them separately based on this probability ranking, and controls the total number of edges with a separate sampling rate $k$. Extensive experiments show that EdgeRefine achieves accuracy comparable to the noise-free baseline and substantially outperforms other privacy-preserving methods across datasets and GNN architectures. Under privacy budget $ε= 2.5$, EdgeRefine improves node classification accuracy over state-of-the-art baselines by 17.8% on ACM under GAT and 19.7% on Cora under GCN. In graph classification, it achieves an average accuracy degradation of around 5% compared to the noise-free baseline. Under graph reconstruction attacks, EdgeRefine maintains relative absolute error levels above 1 across all privacy budgets, averaging 1.962 on Cora and 1.472 on AMAP, indicating strong resilience against privacy leakage.

Regulatory frameworks such as GDPR increasingly require that ML predictions be accompanied by post-hoc explanations, even when raw data and trained models cannot be released. Differential privacy (DP) is the standard mitigation for the residual privacy risk of releasing these explanations. We show that DP is not sufficient: an adversary observing only DP-perturbed GNN explanations can reconstruct hidden graph structure with high accuracy. Our attack, PRIVX, exploits the fact that the Gaussian DP mechanism is a single DDPM forward step at known noise level σ(ε), recasting reconstruction as reverse diffusion conditioned on the corrupted signal, a principled Bayesian denoiser under known DP corruption. We formalise a stratified adversary model parameterised by (M, \hatε, \hatδ, S, ρ) that interpolates between oblivious and oracle attackers, and derive endpoint-matched two-sided bounds on reconstruction AUC. For practitioners, we provide regime-stratified guidance on explainer choice: on homophilic graphs, neighbourhood-aggregating explainers (GraphLIME, GNNExplainer) leak more structure than per-node gradient explainers under the same DP budget; on strongly heterophilic graphs the ordering reverses. We introduce PRIVF as an auxiliary diagnostic sharing the same diffusion backbone to decompose leakage into explainer-induced and intrinsic graph-distribution components. Experiments across seven benchmarks, three DP mechanisms, and three GNN backbones show PRIVX achieves AUC above 0.7 at ε = 5 on five of seven datasets, with the attack succeeding well within typically deployed privacy budgets.

Existing privacy analyses for Graph Neural Networks (GNNs) largely inherit assumptions from non-graph settings, overlooking structural correlations and stochastic training-graph sampling. In particular, node-dependent priors make type-I and type-II errors alone insufficient to characterize the best membership inference test. To address this, we introduce Bayesian Membership Privacy (BMP), a sampling-aware formulation of node-level membership privacy that incorporates node-dependent priors and treats graph sampling probabilities as part of the adversary's knowledge. BMP casts membership inference as a Bayesian hypothesis test and accordingly quantifies membership privacy in terms of posterior membership probability. We explore theoretical properties of BMP in relation to the existing definitions in the literature. We further propose a practical, sampling-aware auditing mechanism to estimate the parameters of BMP as a measure of node-level privacy leakage in GNNs. We conduct experiments on benchmark graph datasets and show that BMP yields fine-grained privacy insights that are not visible through global attack accuracy alone.