Note for Biochemical/Electrochemical/Physicochemical Hypergraphs and Superhypergraphs

A Chemical Graph represents a molecule where atoms are vertices and chemical bonds are edges, thereby modeling molecular structure mathematically (cf. [1–5]). A Chemical Hypergraph is a specialized multilevel hypergraph that models an entire chemical system by representing atoms, chemical bonds, molecules, and reactions as layered hyperedges across different levels (cf. [6–8]). A Chemical Superhypergraph is a hierarchical, multi-level structure that models atoms, chemical bonds, molecular substructures, complete molecules, and higher-order aggregates as nested hyperedges, each associated with quantitative weights. In this paper, we investigate whether new concepts such as the Biochemical Graph, Electrochemical Graph, Physicochemical Graph, and Medichemical Graph can be formally defined. We also explore whether their corresponding HyperGraph and SuperHyperGraph extensions can be constructed. This work is primarily a theoretical study conducted at a conceptual level; however, we expect that future research by domain experts will further examine the practical effectiveness and applications of these proposed frameworks.