Pure Mathematics for Theoretical Computer Science PMTCS 2995-3162 10.54216/PMTCS https://www.americaspg.com/journals/show/3833 2023 2023 Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan Takaaki Takaaki 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 2025 21 33 10.54216/PMTCS.050103 https://www.americaspg.com/articleinfo/40/show/3833