DHMNN: A Hypergraph Motif-Based Framework for Directed Hyperlink Prediction.

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.