Chemical Hypergraph and Chemical SuperHyperGraph

Graph theory introduces vertices and edges to capture binary relationships among entities [1]. A hypergraph extends this concept by allowing hyperedges to connect arbitrarily many vertices, thereby modeling complex multi-way relationships [2]. The recently proposed SuperHyperGraph further generalizes hypergraphs by incorporating iterated powerset layers, and has attracted considerable attention [3, 4]. In chemical graph theory, a Chemical Graph represents molecules as graphs with atoms as vertices and bonds as edges [5–9], whereas a Chemical Hypergraph models entire chemical systems by representing atoms, bonds, molecular assemblies, and reactions as layered hyperedges across multiple levels [10–12]. In this paper, we introduce the Chemical SuperHyperGraph, which extends the Chemical Hypergraph within the SuperHyperGraph framework, and investigate its fundamental definitions and properties. We also define the Chemical Reaction SuperHyperGraph, an extension of the Chemical Reaction HyperGraph via SuperHyperGraphs, and examine its structural characteristics. We anticipate that these new concepts will advance the study of both chemistry and graph theory.