Topology-Aware Gaussian Graph Repair for Robust Graph Neural Networks

2026-06-02

AI Summary

Real-world graph data often suffer from noisy or missing edges, which degrade the performance of graph neural networks (GNNs); existing methods struggle to effectively address both issues simultaneously. This work proposes TAGR, a lightweight sparse graph refinement framework that enhances GNN robustness without modifying its architecture. TAGR constructs a feature-based adjacency graph using an adaptive Gaussian kernel and incorporates a topology-aware residual correction mechanism to efficiently and stably repair graph structure. By jointly leveraging local feature similarity and structural consistency, the method avoids generating dense graphs while significantly improving GNN performance on noisy or incomplete graphs. Extensive experiments on standard citation network benchmarks demonstrate the effectiveness and superiority of the proposed approach.

Abstract

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.

Problem

• graph neural networks
• noisy edges
• missing edges
• graph topology
• robustness

Innovation

• Graph Repair
• Gaussian Kernel
• Topology-Aware
• Robust GNNs
• Sparse Graph Learning