HyperWeighted Graph, SuperHyperWeighted Graph, and MultiWeighted Graph

A weighted graph is a graph in which each edge is assigned a numerical value (weight), typically representing cost, distance, or intensity. In this paper, we revisit and further explore three generalizations of weighted graphs: the Hyperweighted Graph, the Superhyperweighted Graph, and the MultiWeighted Graph. These advanced structures were initially introduced. Our objective is to enhance understanding and broaden awareness of their theoretical foundations and potential applications through renewed analysis and formal refinement.