| _version_ | 1866901913352536064 |
|---|---|
| author | Fujita, Takaaki |
| author_facet | Fujita, Takaaki |
| contents | <p>Abstract. A finite hypergraph generalizes an ordinary graph by permitting a hyperedge to connect any<br>nonempty subset of vertices, thereby capturing multiway interactions. Extending this idea, a finite Super<br>HyperGraph is obtained by iterating the powerset operation, producing nested families of vertex and edge<br>sets that model multi-layer relational structure. Separately, a conceptual graph is a labeled bipartite graph<br>whose concept nodes and relation nodes encode typed relations with ordered arguments, while a conceptual<br>hypergraph represents relation instances as typed hyperedges incident to an ordered tuple of vertices. In this<br>paper, we extend these conceptual formalisms using the SuperHyperGraph framework, introducing Conceptual<br>SuperHyperGraphs and examining their basic properties.</p> <p><br>Keywords: Conceptual HyperGraph, Conceptual SuperHyperGraph, HyperGraph, SuperHyperGraph</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19428419 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Conceptual HyperGraph and Conceptual SuperHyperGraph Fujita, Takaaki <p>Abstract. A finite hypergraph generalizes an ordinary graph by permitting a hyperedge to connect any<br>nonempty subset of vertices, thereby capturing multiway interactions. Extending this idea, a finite Super<br>HyperGraph is obtained by iterating the powerset operation, producing nested families of vertex and edge<br>sets that model multi-layer relational structure. Separately, a conceptual graph is a labeled bipartite graph<br>whose concept nodes and relation nodes encode typed relations with ordered arguments, while a conceptual<br>hypergraph represents relation instances as typed hyperedges incident to an ordered tuple of vertices. In this<br>paper, we extend these conceptual formalisms using the SuperHyperGraph framework, introducing Conceptual<br>SuperHyperGraphs and examining their basic properties.</p> <p><br>Keywords: Conceptual HyperGraph, Conceptual SuperHyperGraph, HyperGraph, SuperHyperGraph</p> |
| title | Conceptual HyperGraph and Conceptual SuperHyperGraph |
| url | https://doi.org/10.5281/zenodo.19428419 |