aspg-40-3833-1792469568 20261020041248 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Pure Mathematics for Theoretical Computer Science PMTCS 2995-3162 2025 5 1 Takaaki Fujita Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan 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 in.10 Our objective is to enhance understanding and broaden awareness of their theoretical foundations and potential applications through renewed analysis and formal refinement 2025 14 22 3833 https://creativecommons.org/licenses/by/4.0/ 10.54216/PMTCS.050103 https://www.americaspg.com/journal/40/article/3833 https://www.americaspg.com/storage/articles/manuscripts/01M11Z7JHVPPD3GB3FVRZ7K4A6.pdf