SuperHyperGraph neural network and dynamic SuperHyperGraph neural network

Graph theory explores the relationships between objects through mathematical structures composed of vertices (nodes) and edges (connections). A hypergraph generalizes the classical graph by introducing hyperedges, which can connect any number of vertices rather than just two, thus enabling the modeling of more complex multi-way relationships [3,20,21]. Building upon this, the concept of a SuperHyperGraph has been introduced as a further extension of hypergraphs and has recently become a subject of active research [1, 5, 17, 44]. Graph Neural Networks (GNNs) are one of the most extensively studied frameworks in artificial intelligence [2, 22, 29, 48]. The HyperGraph Neural Network (HGNN) extends GNNs by leveraging the expressive power of hypergraphs [27, 52]. In this paper, we provide a concise introduction to the 𝑛-SuperHyperGraph Neural Network as defined in [18], which mathematically extends the HGNN architecture using SuperHyperGraphs. We also explore the concept of a Dynamic 𝑛-SuperHyperGraph Neural Network, inspired by the ideas behind Dynamic Graph Neural Networks and Dynamic HyperGraph Neural Networks. We anticipate that these formal developments will pave the way for future computational experiments on real-world datasets.