<p>HyperWeighted Graph, SuperHyperWeighted Graph, and</p>
<p>MultiWeighted Graph</p>
<p>Takaaki Fujita 1,&lowast;</p>
<p>1Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan</p>
<p>Email: takaaki.fujita060@gmail.com</p>
<p>Abstract</p>
<p>A weighted graph is a graph in which each edge is assigned a numerical value (weight), typically representing</p>
<p>cost, distance, or intensity. In this paper, we revisit and further explore three generalizations of weighted</p>
<p>graphs: the Hyperweighted Graph, the Superhyperweighted Graph, and the MultiWeighted Graph. These</p>
<p>advanced structures were initially introduced in.10 Our objective is to enhance understanding and broaden</p>
<p>awareness of their theoretical foundations and potential applications through renewed analysis and formal</p>
<p>refinement.</p>
<p>Keywords: HyperWeighted Graph; SuperHyperWeighted Graph; Weighted Graph; Weighted Set</p>