Graph Robustness

Signed graph learning has emerged as a powerful framework for modeling networks with both positive and negative interactions. While graph-filter-based methods have achieved promising empirical performance on signed networks, their stability under edge perturbations remains less well understood. Existing stability analyses primarily focus on unsigned graphs and do not account for sign-flip perturbations. In this paper, we study the stability of signed graph filters under edge additions, deletions, and sign flips. Our theoretical analysis reveals how signed edge perturbations and node feature correlations jointly determine the learned representation stability. Based on this analysis, we propose a theory-guided perturbation strategy that selects structurally influential signed-edge modifications. Experiments on synthetic and real signed graphs show that the proposed method consistently induces larger embedding drift, polarity change, and downstream link prediction degradation than baselines. These results highlight the importance of sign-aware and distribution-aware stability analysis for signed graph learning.

Zero-shot graph models (ZGMs), which learn transferable knowledge from source graphs and directly apply to unseen target graphs without any adaptation, have achieved promising performance and attracted considerable attention. Despite their proliferation, existing ZGMs are predominantly evaluated on clean graphs, while existing graph robustness benchmarks mainly focus on supervised settings, leaving a fundamental question largely unexplored: How robust are ZGMs when their unseen target graphs are exposed to adversarial manipulation? In this paper, we answer this question by proposing ZeroGAR, the first systematic benchmark for evaluating the adversarial robustness of ZGMs. ZeroGAR evaluates 13 representative ZGMs from 3 different paradigms on 8 graph datasets across 4 domains, covering both in-domain and cross-domain transfer under structural, textual, and node injection attacks with multiple perturbation budgets. It further investigates whether existing graph defenses remain effective in the zero-shot setting. Extensive experiments reveal that strong clean zero-shot performance does not guarantee adversarial robustness, with three key findings: (1) Vulnerability patterns are related to model prediction mechanisms: GNN-based methods are particularly vulnerable to structural and node injection attacks, whereas LLM-based methods are more vulnerable to textual attacks; (2) Stronger LLM backbones introduce a structure-text robustness trade-off; (3) Existing graph defense methods do not consistently improve zero-shot robustness and may compromise clean performance. We hope that ZeroGAR will facilitate rapid, equitable evaluation and inspire further innovative research in ZGM security.

Rapid evaluation of many simultaneous road-link disruptions requires a practical compromise between exact spectral recomputation and local approximation. We estimate relative algebraic-connectivity loss after multi-edge deletion using graph neural networks (GNNs) that learn a bounded correction to a first-order Fiedler sensitivity. The study considers independent, spatially clustered, and edge-betweenness-targeted failures, with graph-disjoint synthetic splits and zero-shot transfer to 13 OpenStreetMap (OSM) areas in six countries. GCN, GraphSAGE, and edge-aware MPNN backbones are compared with analytical baselines. In expanded OSM tests, residual GCN improves spatial-failure MAE by 0.0391 (95% hierarchical interval 0.0151-0.0662), while residual GraphSAGE improves targeted-failure MAE by 0.0257 (0.0095-0.0446). Second-order perturbation improves first-order MAE by only 0.0028-0.0053. Correction slopes decrease under targeted transfer, indicating residual shrinkage around systematic prior error. Leave-one-country-out OSM-to-OSM transfer is mixed: residual GCN improves targeted-failure MAE by 0.0622 (0.0169-0.1153) but worsens the spatial point estimate. Sparse scaling extends to 20,000 nodes and separates one-time spectral setup from amortized screening cost. These results characterize the spectral residual as a useful but domain-sensitive inductive bias for structural connectivity screening. Code, cached networks, and reproducibility artifacts are archived at doi:10.5281/zenodo.22307723.

Spectral graph neural networks (GNNs) interpret message passing as frequency-selective filtering. While low-order spectral filters are efficient, their limited selectivity often leads to weak attenuation outside the passband, whereas high-order alternatives introduce optimization challenges. We propose DCQ-GNN, a spectral GNN based on a compact bank of adaptive convex--concave quadratic filters. By restricting the filter order to two while explicitly exploiting complementary curvature, DCQ-GNN improves spectral selectivity as quantified by Dirichlet energy and entropy measures without resorting to high-order polynomial expansions. The model fuses filter outputs through a node-adaptive gating mechanism to enable node-wise structure-aware spectral selection. We provide a formal spectral analysis grounded in Dirichlet energy attenuation, von Neumann entropy, and curvature polarity, and derive explicit characterizations of filter behavior across varying levels of homophily and structural perturbations. Extensive benchmarks on 10 datasets show that DCQ-GNN ties for the top average rank (3.0) on heterophilic graphs and obtains the second-best rank (4.2) on homophilic graphs, remaining competitive with representative high-order polynomial spectral filters. Furthermore, under strong structural perturbations, DCQ-GNN exhibits substantially smaller performance degradation compared to both first-order and high-order baselines. These results demonstrate that curvature-aware quadratic banks provide a robust and efficient alternative to high-order spectral models while preserving optimization stability and computational efficiency.

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 representation learning (GRL) has evolved from topology-only graph embeddings to task-specific supervised GNNs, and more recently to reusable representations and graph foundation models (GFMs). However, existing evaluations mainly measure clean transfer, adaptation, and task coverage. It remains unclear whether GRL methods stay reliable when deployment stresses affect graph signals, graph contexts, label support, structural groups, or predictive evidence. We introduce GRL-Safety, a multi-axis safety evaluation benchmark for GRL. GRL-Safety evaluates twelve representative methods, spanning topology-only embedding methods, supervised GNNs, self-supervised graph models, and GFMs, on twenty-five graph datasets under standardized evaluation conditions while preserving method-native adaptation. The evaluation covers five safety axes: corruption robustness, OOD generalization, class imbalance, fairness, and interpretation, with per-axis and sub-condition reporting rather than a single aggregate score. Our analysis yields three cross-axis insights that can inspire future research. First, safety behavior is shaped by the interaction between representation design and the stressed graph factor, rather than by method family alone. Second, foundation-era methods show axis-specific strengths rather than broad safety dominance. Third, several deployment regimes remain difficult even for the best evaluated method, revealing capability gaps that require new robustness, adaptation, or training objectives beyond model selection. The benchmark, evaluation protocols, and code are available at: https://github.com/GXG-CS/GRL-Safety.

Knowledge graphs automatically constructed from text are increasingly used in real-world applications. However, their inherent noise, fragmentation, and semantic inconsistencies significantly affect the performance of Graph Neural Networks (GNNs) on downstream tasks. Assessing their performance and robustness remains difficult, as it is often unclear whether observed results stem from the learning model or from the quality of the constructed graph itself. In this work, we introduce a dual-purpose benchmark designed to jointly evaluate (i) the performance of GNNs on noisy, text-derived graphs and (ii) the effectiveness of graph construction methods on a downstream task. The benchmark is built in the biomedical domain from a single textual corpus and includes two automatically constructed graphs generated using different extraction methods, alongside a high-quality reference graph curated by experts that serves as an upper performance bound. This design enables controlled comparison of construction methods and systematic evaluation of GNN robustness through semi-supervised node classification. We further provide a standardized, reproducible, and extensible evaluation framework, facilitating the integration of new graph extraction methods and learning models.

Spectral graph contrastive learning often constructs low- and high-frequency views to capture complementary graph signals, but these views are commonly combined by graph-level or node-agnostic fusion rules. We show that graph-level fusion can incur irreducible regret on mixed graphs with separated node-wise spectral preferences. Motivated by this result, we propose ASPECT, a spectral graph contrastive learning method that adaptively fuses low- and high-frequency views at the node level. ASPECT learns a node-wise spectral policy and regularizes it using channel-wise contrastive evidence, enabling different nodes to use different spectral mixtures. We further introduce ASPECT-S, an optional stability-aware extension that uses generated graph-structure and feature perturbations to obtain empirical channel-wise sensitivity estimates, together with a Rayleigh-based spectral search bias for producing informative perturbations. Experiments on homophilic and heterophilic benchmarks show that ASPECT improves representation quality over competitive spectral and graph contrastive baselines, while ASPECT-S further improves performance under joint graph-structure and feature perturbations.

While graph-derived signals are widely used in tabular learning, existing studies typically rely on limited experimental setups and average performance comparisons, leaving the statistical reliability and robustness of observed gains largely unexplored. Consequently, it remains unclear which signals provide consistent and robust improvements. This paper presents a taxonomy-driven empirical analysis of graph-derived signals for tabular machine learning. We propose a unified and reproducible evaluation protocol to systematically assess which categories of graph-derived signals yield statistically significant and robust performance improvements. The protocol provides an extensible setup for the controlled integration of diverse graph-derived signals into tabular learning pipelines. To ensure a fair and rigorous comparison, it incorporates automated hyperparameter optimization, multi-seed statistical evaluation, formal significance testing, and robustness analysis under graph perturbations. We demonstrate the protocol through an extensive case study on a large-scale, imbalanced cryptocurrency fraud detection dataset. The analysis identifies signal categories providing consistently reliable performance gains and offers interpretable insights into which graph-derived signals indicate fraud-discriminative structural patterns. Furthermore, robustness analyses reveal pronounced differences in how various signals handle missing or corrupted relational data. These findings demonstrate practical utility for fraud detection and illustrate how the proposed taxonomy-driven evaluation protocol can be applied in other application domains.

In order to evaluate the invulnerability of networks against various types of attacks and provide guidance for potential performance enhancement as well as controllability maintenance, network controllability robustness (NCR) has attracted increasing attention in recent years. Traditionally, controllability robustness is determined by attack simulations, which are computationally time-consuming and only applicable to small-scale networks. Although some machine learning-based methods for predicting network controllability robustness have been proposed, they mainly focus on pairwise interactions in complex networks, and the underlying relationships between high-order structural information and controllability robustness have not been explored. In this paper, a dual hypergraph attention neural network model based on high-order knowledge (NCR-HoK) is proposed to accomplish robustness learning and controllability robustness curve prediction. Through a node feature encoder, hypergraph construction with high-order relations, and a dedicated dual hypergraph attention module, the proposed method can effectively learn three types of network information simultaneously: explicit structural information in the original graph, high-order connection information in local neighborhoods, and hidden features in the embedding space. Notably, we explore for the first time the impact of high-order knowledge on network controllability robustness. Compared with state-of-the-art methods for network robustness learning, the proposed method achieves superior performance on both synthetic and real-world networks with low computational overhead.

Existing research on robust Graph Neural Networks (GNNs) focuses predominantly on undirected graphs, overlooking the trustworthiness inherent in the link directions of directed graphs. In this work, we analyze the limitations of current approaches from both the attack and defense perspectives and redefine the robustness of GNNs in directed graphs. From the attack side, we introduce a more realistic directed graph attack setting that addresses the shortcomings of existing attacks. From the defense side, we propose a simple yet effective message-passing framework that serves as a plug-in layer to strengthen GNN robustness while avoiding a false sense of robustness. Our findings show that the trust signals encoded in directed graphs can be harnessed to substantially improve the robustness of GNNs. When combined with existing defense strategies, the framework achieves state-of-the-art robust performance alongside strong clean accuracy against both transfer and adaptive attacks. These results point to a novel and promising direction for strengthening the robustness of graph deep learning.