Hyperweighted and Superhyperweighted MultiGraphs: Foundations and Real-World Applications

Takaaki Fujita

doi:10.22105/scfa.vi.52

Authors

Takaaki Fujita * Independent Researcher

https://doi.org/10.22105/scfa.vi.52

Abstract

A weighted graph is a graph in which each edge carries a numerical weight, typically representing cost, distance, or intensity. Recently, the notions of the Hyperweighted Graph and the Superhyperweighted Graph were introduced.
A Hyperweighted Graph is a graph where each edge is assigned a nonempty set of real‐valued weights, capturing multiple metrics simultaneously (e.g., distance, cost). A Superhyperweighted Graph assigns each edge a nested hierarchy of weight‐sets (sets of sets of real numbers), enabling multi‐level attribute modeling. Extensive research has also been conducted on weighted MultiGraphs.

In this paper, we extend these ideas by exploring the classes of Hyperweighted MultiGraphs and Superhyperweighted MultiGraphs, and analyzing their fundamental properties. This concept extends weighted MultiGraphs by incorporating the notions of Hyperweighted Graphs and Superhyperweighted Graphs. We expect that these extensions will stimulate further research on graph algorithms and real‐world applications of graph theory.

Keywords

Weighted Graph Uncertain Graph Graph Theory HyperWeighted Graph

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Hyperweighted and Superhyperweighted MultiGraphs: Foundations and Real-World Applications

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