Recursive HyperGraphs and Recursive SuperHyperGraphs: Exploring More Hierarchical and Generalized Graph Concepts
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| Natura: | Recurso digital |
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Zenodo
2026
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| _version_ | 1866901947314864128 |
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| author | Fujita, Takaaki |
| author_facet | Fujita, Takaaki |
| contents | <p>Abstract. A finite hypergraph generalizes an ordinary graph by allowing a hyperedge to join any nonempty<br>subset of vertices, thereby capturing genuine multiway interactions. Building on this idea, a finite SuperHyper<br>Graph is obtained by iterating the powerset construction, so that set-valued objects created at one level may<br>serve as vertices or edge endpoints at the next, yielding a principled representation of hierarchical and multi<br>layer relational structure. In a different direction, a Recursive HyperGraph permits hyperedges to contain not<br>only ordinary vertices but also lower-level hyperedges as elements, enabling nested, self-referential incidence up<br>to a prescribed recursion depth. In this paper, we integrate these two extensions: we formalize recursion within<br>the SuperHyperGraph setting and introduce the notion of a Recursive SuperHyperGraph, which simultaneously<br>captures vertex hierarchy and recursive edge nesting.</p> <p><br>Keywords: Recursive SuperHyperGraph, HyperGraph, SuperHyperGraph, Recursive HyperGraph</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19428386 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Recursive HyperGraphs and Recursive SuperHyperGraphs: Exploring More Hierarchical and Generalized Graph Concepts Fujita, Takaaki <p>Abstract. A finite hypergraph generalizes an ordinary graph by allowing a hyperedge to join any nonempty<br>subset of vertices, thereby capturing genuine multiway interactions. Building on this idea, a finite SuperHyper<br>Graph is obtained by iterating the powerset construction, so that set-valued objects created at one level may<br>serve as vertices or edge endpoints at the next, yielding a principled representation of hierarchical and multi<br>layer relational structure. In a different direction, a Recursive HyperGraph permits hyperedges to contain not<br>only ordinary vertices but also lower-level hyperedges as elements, enabling nested, self-referential incidence up<br>to a prescribed recursion depth. In this paper, we integrate these two extensions: we formalize recursion within<br>the SuperHyperGraph setting and introduce the notion of a Recursive SuperHyperGraph, which simultaneously<br>captures vertex hierarchy and recursive edge nesting.</p> <p><br>Keywords: Recursive SuperHyperGraph, HyperGraph, SuperHyperGraph, Recursive HyperGraph</p> |
| title | Recursive HyperGraphs and Recursive SuperHyperGraphs: Exploring More Hierarchical and Generalized Graph Concepts |
| url | https://doi.org/10.5281/zenodo.19428386 |