An Introduction and Reexamination of Molecular Hypergraph and Molecular n-SuperHypergraph

Abstract

A molecular graph is a labeled graph in which atoms are represented by vertices and covalent bonds by edges, with each edge labeled according to the bond type (Gasteiger et al., 2020). A hypergraph generalizes the concept of a traditional graph by allowing edges—called hyperedges—to connect more than two vertices simultaneously (Berge, 1984). A superhypergraph further extends this idea by incorporating recursively defined powerset layers, enabling hierarchical and self-referential relationships among hyperedges (Smarandache, 2020). This paper investigates the formalization, illustrative examples, and structural properties of molecular hypergraphs and molecular superhypergraphs (cf. (Fujita, 2025c)). These constructs, grounded in the theoretical foundations of hypergraphs and superhypergraphs, provide enriched frameworks for representing molecular systems and facilitate deeper exploration of hierarchical chemical connectivity and molecular structure.