[2412.01176] Theoretical Foundations of Superhypergraph and Plithogenic Graph Neural Networks

Computer Science > Artificial Intelligence arXiv:2412.01176 (cs) [Submitted on 2 Dec 2024 (v1), last revised 2 Mar 2026 (this version, v2)] Title:Theoretical Foundations of Superhypergraph and Plithogenic Graph Neural Networks Authors:Takaaki Fujita, Florentin Smarandache View a PDF of the paper titled Theoretical Foundations of Superhypergraph and Plithogenic Graph Neural Networks, by Takaaki Fujita and Florentin Smarandache View PDF Abstract:Hypergraphs generalize classical graphs by allowing a single edge to connect multiple vertices, providing a natural language for modeling higher-order interactions. Superhypergraphs extend this paradigm further by accommodating nested, set-valued entities and relations, enabling the representation of hierarchical, multi-level structures beyond the expressive reach of ordinary graphs or hypergraphs. In parallel, neural networks-especially Graph Neural Networks (GNNs)-have become a standard tool for learning from relational data, and recent years have seen rapid progress on Hypergraph Neural Networks (HGNNs) and their theoretical properties. To model uncertainty and multi-aspect attributes in complex networks, several graded and multi-valued graph frameworks have been developed, including fuzzy graphs and neutrosophic graphs. The plithogenic graph framework unifies and refines these approaches by incorporating multi-valued attributes together with membership and contradiction mechanisms, offering a flexible representation for heterogen...