Molecular Fuzzy graphs, hypergraphs, and superhypergraphs

Graph theory provides a framework for clearly representing relationships between objects [1,2]. In the fields of chemistry and biology, graph-based concepts are widely applied. Hypergraphs generalize classical graphs by allowing hyperedges to connect any nonempty subset of vertices [3]. Superhypergraphs extend this concept by iterating the powerset operation, thereby generating nested layers that capture hierarchical and self-referential structures among collections of vertices [4]. A molecular graph models a molecule with atoms as vertices and bonds as edges, representing its structural connectivity. Fuzzy graphs and fuzzy hypergraphs enrich these structures by assigning membership degrees to vertices and (hyper)edges. In this paper, we introduce definitions of molecular fuzzy graphs, hypergraphs, and superhypergraphs, and examine their properties and potential applications.