Harnessing Trust in Directed Graphs: Redefining Robustness of Graph Learning

Graph neural networks have achieved strong performance on graph-structured data, but their effectiveness depends heavily on the quality of the observed graph. In real applications, graph topology is often imperfect: noisy edges may connect unrelated nodes, while missing edges may prevent useful information from being propagated. Existing robust graph learning methods mainly address this problem by removing suspicious edges or by learning a new graph structure during training. However, edge removal alone cannot recover missing connections, and graph structure learning may introduce additional optimization complexity. In this paper, we propose Topology-Aware Gaussian Repair (TAGR), a simple graph repair framework for robust message passing in graph neural networks. Instead of learning a dense adjacency matrix, TAGR constructs a sparse feature-neighborhood graph using an adaptive Gaussian kernel and combines it with a topology-aware residual correction of the observed graph. The Gaussian repair component introduces auxiliary edges between feature-similar nodes, while the residual correction preserves and reweights the original topology according to local feature and structural consistency. The repaired graph can be used directly with standard graph neural networks without changing their architectures. Extensive experiments on benchmark citation networks show that TAGR improves the robustness of GNNs under both noisy-edge and missing-edge settings. The analysis further show that Gaussian feature-neighborhood repair provides the main robustness gain, while topology-aware residual correction improves stability when the observed graph is incomplete. These results suggest that effective graph robustness can be achieved through lightweight sparse graph repair rather than dense graph structure learning.

Graph Neural Networks (GNNs) are vulnerable to adversarial attacks, which inherently invert connectivity patterns by introducing disassortative edges in assortative graphs and assortative edges in disassortative graphs. This structural inversion creates structure-feature mismatches that disrupt neighborhood aggregation across different graph types. However, we find that existing defenses are limited, as they either treat neighborhoods as monolithic under fixed assortativity assumptions or rely on standard softmax classifiers that fail to account for perturbation-induced representation shifts. To further exploit this observation, we adopt a robustness perspective that jointly disentangles node representations and decision spaces, isolating perturbation effects while enforcing well-separated decision regions. Based on this principle, we propose Graph Joint Disentanglement Network (GJDNet), a unified framework for robust node classification across diverse graph assortativity regimes. GJDNet enhances robustness at both representation and decision levels: it employs feature-driven soft structural disentanglement with skewness-aware neighbor filtering to suppress perturbation-induced structure-feature mismatches, and introduces a Spherical Decision Boundary (SDB) to promote intra-class compactness and inter-class separation in the embedding space, thereby stabilizing decision boundaries under perturbations. Theoretical analysis provides insights into the effectiveness of the proposed disentangled representation and decision mechanisms, while extensive experiments demonstrate that GJDNet consistently achieves strong robustness across graphs with different connectivity regimes.

Graph neural network (GNN) is a powerful tool for analyzing graph-structured data. However, their vulnerability to adversarial attacks raises serious concerns, especially when dealing with sensitive information. Local Differential Privacy (LDP) offers a privacy-preserving framework for training GNNs, but its impact on adversarial robustness remains underexplored. This paper investigates adversarial attacks on LDP-protected GNNs. We explore how the privacy guarantees of LDP can be leveraged or hindered by adversarial perturbations. The effectiveness of existing attack methods on LDP-protected GNNs are analyzed and potential challenges in crafting adversarial examples under LDP constraints are discussed. Additionally, we suggest directions for defending LDP-protected GNNs against adversarial attacks. This work investigates the interplay between privacy and security in graph learning, highlighting the need for robust and privacy-preserving GNN architectures.