2836-4449ISSN (Online)
Volume 5 , Issue 1 , PP: 12-31, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Takaaki Fujita 1 * , Atiqe Ur Rahman 2 , Arkan A. Ghaib 3 , Talal Ali Al-Hawary 4 , Arif Mehmood Khattak 5
Doi: https://doi.org/10.54216/PAMDA.050102
In graph theory, a hypergraph generalizes a classical graph by allowing each hyperedge to join any number of vertices, thereby modeling relationships beyond simple pairwise connections.[1] A superhypergraph takes this further by applying recursive powerset constructions to its hyperedge set, creating hierarchical and self-referential network layers.[2] A soft graph defines a family of subgraphs parameterized over a fixed universe of vertices and edges, while a rough graph uses lower and upper approximations to capture uncertainty in graph structure. In this paper, we revisit Soft SuperHypergraphs and Rough SuperHypergraphs—originally introduced in [3]—which integrate the flexibility of soft and rough graph frameworks with the layered com- plexity of superhypergraphs. We provide precise definitions, illustrative examples, and a detailed analysis of their fundamental properties, demonstrating their potential for modeling hierarchical and uncertain network systems.
Superhypergraph , Hypergraph , Soft Graph , Rough Graph , Soft HyperGraph , Rough HyperGraph
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