Out-of-distribution (OOD) detection plays a critical role in ensuring the robustness of machine learning models in open-world settings. While extensive efforts have been made in vision, language, and graph domains, the challenge of OOD detection in hypergraph-structured data remains unexplored. In this work, we formalize the problem of hypergraph out-of-distribution (HOOD) detection, which aims to identify nodes or hyperedges whose high-order relational contexts differ significantly from those seen during training. We propose HyperGOOD, a unified energy-based detection framework that integrates multi-scale spectral decomposition with structure-aware uncertainty propagation. By preserving both low- and high-frequency signals and diffusing uncertainty across the hypergraph, HyperGOOD effectively captures subtle and relationally entangled anomalies. Experimental results on nine hypergraph datasets demonstrate the effectiveness of our approach, establishing a new foundation for robust hypergraph learning under distributional shifts.

The out-of-distribution (OOD) detection on graph-structured data is crucial for deploying graph neural networks securely in open-world scenarios. However, existing methods have overlooked the prevalent scenario of multi-label classification in real-world applications. In this work, we investigate the unexplored issue of OOD detection within multi-label node classification tasks. We propose ML-GOOD, a simple yet sufficient approach that utilizes an energy function to gauge the OOD score for each label. We further develop a strategy for amalgamating multiple label energies, allowing for the comprehensive utilization of label information to tackle the primary challenges encountered in multi-label scenarios. Extensive experimentation conducted on seven diverse sets of real-world multi-label graph datasets, encompassing cross-domain scenarios. The results show that the AUROC of ML-GOOD is improved by 5.26% in intra-domain and 6.54% in cross-domain compared to the previous methods. These empirical validations not only affirm the robustness of our methodology but also illuminate new avenues for further exploration within this burgeoning field of research.

With the growing adoption of Hypergraph Neural Networks (HNNs) to model higher-order relationships in complex data, concerns about their security and robustness have become increasingly important. However, current security research often overlooks the unique structural characteristics of hypergraph models when developing adversarial attack and defense strategies. To address this gap, we demonstrate that hypergraphs are particularly vulnerable to node injection attacks, which align closely with real-world applications. Through empirical analysis, we develop a relatively unnoticeable attack approach by monitoring changes in homophily and leveraging this self-regulating property to enhance stealth. Building on these insights, we introduce HyperNear, i.e., $\underline{N}$ode inj$\underline{E}$ction $\underline{A}$ttacks on hype$\underline{R}$graph neural networks, the first node injection attack framework specifically tailored for HNNs. HyperNear integrates homophily-preserving strategies to optimize both stealth and attack effectiveness. Extensive experiments show that HyperNear achieves excellent performance and generalization, marking the first comprehensive study of injection attacks on hypergraphs. Our code is available at https://github.com/ca1man-2022/HyperNear.

Heterophilic graph neural networks (GNNs) have gained prominence for their ability to learn effective representations in graphs with diverse, attribute-aware relationships. While existing methods leverage attribute inference during message passing to improve performance, they often struggle with challenging heterophilic graphs. This is due to edge distribution shifts introduced by diverse connection patterns, which blur attribute distinctions and undermine message-passing stability. This paper introduces H₂OGNN, a novel framework that reframes edge attribute inference as an out-of-distribution (OOD) detection problem. H₂OGNN introduces a simple yet effective symbolic energy regularization approach for OOD learning, ensuring robust classification boundaries between homophilic and heterophilic edge attributes. This design significantly improves the stability and reliability of GNNs across diverse connectivity patterns. Through theoretical analysis, we show that H₂OGNN addresses the graph denoising problem by going beyond feature smoothing, offering deeper insights into how precise edge attribute identification boosts model performance. Extensive experiments on nine benchmark datasets demonstrate that H₂OGNN not only achieves state-of-the-art performance but also consistently outperforms other heterophilic GNN frameworks, particularly on datasets with high heterophily.