Aug 2026· IEEE Transactions on Neural Networks and Learning Systems· Vol PP, pp. 1-15· 0 citations
Medicine
TL;DR
A novel directed hypergraph motif-based neural network (DHMNN) for directed hyperlink prediction, which simultaneously captures higher order structural and connectivity information from the directed hypergraph topology and significantly outperforms state-of-the-art models.
Abstract
Directed hypergraphs have gained increasing attention for modeling group interactions while preserving directionality. However, link prediction in directed hypergraphs has rarely been studied despite its practical significance in complex systems analysis. Existing models perform poorly due to three major challenges in directed hypergraphs: 1) lacking effective feature initialization methods; 2) neglecting to detect higher order substructures; and 3) failing to capture long-range dependencies among vertices. To address these challenges, we propose a novel directed hypergraph motif-based neural network (DHMNN) for directed hyperlink prediction, which simultaneously captures higher order structural and connectivity information from the directed hypergraph topology. First, we introduce directed hypergraph motifs (DH-motifs) to explore higher order neighborhoods, analyzing vertex structural equivalence and generating structural features. Secondly, we utilize hypergraph incidence matrices to measure local connectivity, quantifying vertex co-occurrences and producing connectivity features. Then, we employ hypergraph attention to refine the vertex features at both global and local levels, further capturing long- and short-range dependencies. Finally, a new scoring layer is designed to assess the reliability of each link, considering its local properties, feature variance, and directionality. Extensive experiments on seven metabolic networks and three social networks demonstrate that DHMNN significantly and consistently outperforms state-of-the-art models, achieving a 3.40%-9.90% increase in accuracy. Our code is available at: https://github.com/XihangMeng/DHMNN.
Hypergraphs offer a natural paradigm for modeling complex systems with multi-way interactions. Hypergraph neural networks (HGNNs) have demonstrated remarkable success in learning from such higher-order relational data. While such higher-order modeling enhances relational reasoning, the effectiveness of hyper-graph learning remains bottlenecked by two persistent challenges: the scarcity of labeled data inherent to complex systems, and the vulnerability to structural noise in real-world interaction patterns. Traditional data augmentation methods, though successful in Euclidean and graph-structured domains, struggle to preserve the intricate balance between node features and hyperedge semantics, often disrupting the very group-wise interactions that define hypergraph value. To bridge this gap, we present HyperMixup, a hypergraph-aware augmentation framework that preserves higher-order interaction patterns through structure-guided feature mixing. Specifically, HyperMixup contains three critical components: 1) Structure-aware node pairing guided by joint feature-hyperedge similarity metrics, 2) Context-enhanced hierarchical mixing that preserves hyperedge semantics through dual-level feature fusion, and 3) Adaptive topology reconstruction mechanisms that maintain hypergraph consistency while enabling controlled diversity expansion. Theoret-ically, we establish that our method induces hypergraph-specific regularization effects through gradient alignment with hyperedge covariance structures, while providing robustness guarantees against combined node-hyperedge perturbations. Comprehensive experiments across diverse hypergraph learning tasks demonstrate consistent performance improvements over state-of-the-art baselines, with particular effectiveness in low-label regimes. The proposed framework advances hypergraph representation learning by unifying data augmentation with higher-order topological constraints, offering both practical utility and theoretical insights for relational machine learning
Kaixuan Yao, Zhuo Li, Jianqing Liang et al.· Neural Information Processin...· 0 citations
Experiments show that replacing PageRank with alternative centralities yields similar F1-scores while offering notable runtime savings, and that GraphHD-Order remains competitive with the original GraphHD baseline while providing consistent speedups in encoding time.
Isomorphism recognition is crucial for analyzing complex network structures. Traditional methods like Weisfeiler-Lehman (WL) kernels and various GNNs often overlook higher-order interactions essential for practical applications. Besides, hypergraph WL kernels struggle to distinguish uniform-regular hypergraphs due to their focus on neighborhood connectivity without effectively capturing unique higher-order structures. To overcome these issues, we introduce the Hypergraph Identity-Aware Subtree (IA Subtree) Kernel, which distinguishes uniform-regular hypergraphs by considering both neighborhood connectivity and connection density. This kernel detects subtle differences in hypergraph structures via variations in Closed Paths of different lengths. Additionally, we develop two Hypergraph Neural Networks: Hypergraph Isomorphism Networks (HGIN) and Identity-Aware Hypergraph Isomorphism Networks (IA-HGIN). These models combine the strengths of the Hypergraph WL subtree kernel with advanced neural architectures, improving classification by integrating features from closed-path distributions. We also provide the first comprehensive theoretical comparison of expressive power between kernel-based methods and neural networks, confirming IA-HGIN's superior performance. Experimental results on eight synthetic and eight real hypergraph datasets validate the effectiveness of our methods over existing State-of-the-Art approaches.
Yifan Feng, Rizhuo Huang, Yifan Zhang et al.· IEEE Transactions on Pattern...· 0 citations
Higher-order networks, represented as hypergraphs, enable direct modeling of multi-body interactions of arbitrary size. Hypergraph representations of real-world systems have been observed to exhibit high \emph{simpliciality} --- the tendency for subsets of hyperedges to also appear as hyperedges --- yet the generative mechanisms responsible for this structure are poorly understood. We introduce a generalized preferential attachment hypergraph model in which both hyperedge size $Y_t$ and the number of new nodes per step $X_t$ are drawn from arbitrary distributions, and derive analytically, using a mean-field approximate master equation approach, that the stationary hyperdegree distribution follows a power law whose exponent depends only on the ratio $p = E[X_t]/E[Y_t]$, independent of the shapes of the underlying distributions. Crucially, both $X_t$ and $Y_t$ can be estimated directly from any timestamped hypergraph dataset via a backward-stepping procedure, enabling the model to be fit without parametric assumptions. Applying a nonlinear extension of the model to eight real-world hypergraph datasets, we find that the simplicial fraction increases monotonically with the strength of preferential attachment up to the gelation transition at $\alpha>1$, establishing preferential attachment as a simpliciality-enforcing mechanism.
Understanding hypergraph evolution is essential for revealing high-order interaction patterns and generating credible synthetic data when real interaction records are scarce. Existing models suffer from two key limitations: (1) they rely on global topological heuristics that treat nodes as passive entities, yielding poor semantic consistency and generalization; (2) they ignore the influence of node attributes on structural evolution. We propose HyMAGE, a semantic-aware dynamic hypergraph generation framework based on semantic preferential attachment, without any graph-structure pretraining or centralized optimization objective. HyMAGE models each node as an autonomous agent and leverages LLMs for local-level semantic selection, so that hyperedge formation and dissolution emerge from local semantic affinity and structural context in a self-organizing manner. It serves both as a generative model explaining real-world high-order relationship evolution and as a scalable synthetic data factory that distills LLM domain knowledge into explicit hyperedge structures, producing topology-and-semantics-aligned attributed hypergraphs for downstream tasks. Extensive experiments show that HyMAGE significantly outperforms existing methods at both structural and semantic levels. It simultaneously reproduces nine high-order structural patterns of real hypergraphs and generalizes well to downstream tasks: hypergraph neural networks trained solely on HyMAGE-generated data achieve high accuracy, and its diffusion behaviors closely match those of real hypergraphs. These results demonstrate that HyMAGE offers a plausible explanation for high-order evolution mechanisms while providing rich semantic hypergraph training sets for hypergraph learning and mining.
B. Gu, Ji Zeng, Nuoran Zhou et al.· Proceedings of the 32nd ACM...· 0 citations
This work generalizes three distance-based topological measures, namely closeness centrality, betweenness centrality and node eccentricity, using this new hypergraph distance, and shows that hypergraphs can be divided into three distinct classes, corresponding to the possible dominance of specific orders of interaction over their general metric structure.
E. Vasilyeva, L. Tupikina, D. Musatov et al.· Chaos, Solitons & Fracta...· 0 citations