Theoretical Foundations of Superhypergraph and Plithogenic Graph Neural Networks
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914362140131328 |
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| author | Fujita, Takaaki Smarandache, Florentin |
| author_facet | Fujita, Takaaki Smarandache, Florentin |
| contents | 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 heterogeneous and partially inconsistent information.
This book develops the theoretical foundations of SuperHyperGraph Neural Networks (SHGNNs) and Plithogenic Graph Neural Networks, with the goal of extending message-passing principles to these advanced higher-order structures. We provide rigorous definitions, establish fundamental structural properties, and prove well-definedness results for key constructions, with particular emphasis on strengthened formulations of Soft Graph Neural Networks and Rough Graph Neural Networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01176 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Theoretical Foundations of Superhypergraph and Plithogenic Graph Neural Networks Fujita, Takaaki Smarandache, Florentin Artificial Intelligence Computational Engineering, Finance, and Science Machine Learning Combinatorics Logic 05C65 - Hypergraphs, 05C82 - Graph theory with applications, 03E72 - Fuzzy set theory 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 heterogeneous and partially inconsistent information. This book develops the theoretical foundations of SuperHyperGraph Neural Networks (SHGNNs) and Plithogenic Graph Neural Networks, with the goal of extending message-passing principles to these advanced higher-order structures. We provide rigorous definitions, establish fundamental structural properties, and prove well-definedness results for key constructions, with particular emphasis on strengthened formulations of Soft Graph Neural Networks and Rough Graph Neural Networks. |
| title | Theoretical Foundations of Superhypergraph and Plithogenic Graph Neural Networks |
| topic | Artificial Intelligence Computational Engineering, Finance, and Science Machine Learning Combinatorics Logic 05C65 - Hypergraphs, 05C82 - Graph theory with applications, 03E72 - Fuzzy set theory |
| url | https://arxiv.org/abs/2412.01176 |