We present a unified, set–theoretic framework that extends molecular graphs to hypergraphs and superhypergraphs via iterated power sets. We define Molecular Graphs, Molecular HyperGraphs, and Molecular SuperHyperGraphs, and develop four complements over them: Weighted, Rough, Neural, and Multipolar frameworks. We prove concise inclusion results—most notably, that the Weighted Molecular SuperHyperGraph strictly contains both Weighted Molecular HyperGraphs and (unweighted) Molecular SuperHyperGraphs—while preserving alternating–path distances under canonical embeddings. Compact examples (e.g., methane, ethanol, acetic acid) illustrate how atoms, bonds, functional groups, and higher–order motifs appear as vertices, hyperedges, and superedges under rank constraints. We also provide implementation–agnostic message–passing rules for variable–arity interactions, enabling property prediction and hierarchical analysis in chemistry and chemical biology. This paper is devoted to theoretical analysis, and it is hoped that quantitative studies by domain experts will be developed in future work.
For the first time, the chemical composition of essential oils obtained from the leaves and flowers of Mediterranean rosemary (Salvia rosmarinus) collected in forested areas surrounding Jerusalem has been investigated. Gas chromatographic analysis revealed that the essential oils are dominated by structurally unusual terpenoids containing a cyclobutane ring. A comprehensive survey of the literature further demonstrates that S. rosmarinus is a prolific natural source of cyclobutane-containing terpenes, with approximately 40 such compounds reported to date. These rare terpenoid frameworks are of particular interest due to their uncommon ring strain and distinct biosynthetic origin. In addition, available data on the biological activities of the major cyclobutane-containing terpenes are summarized, highlighting their antimicrobial, anti-inflammatory, antioxidant, and cytotoxic properties. Collectively, these findings underscore rosemary as a unique producer of cyclobutane terpenoids and emphasize the pharmacological potential of this rare class of natural products.
The concept of a classical structure provides a broad mathematical framework, whereas a Hyperstructure arises via the powerset construction, and an n-Superhyperstructure is obtained by iterating this construction n times. Intuitively, the n-th powerset corresponds to n successive applications of the powerset operator. Below, we recall the fundamental definitions and illustrate them with elementary examples. In the chemical sciences, various hyperstructural frameworks—such as Chemical Hyperstructures—have also been studied. In this paper, we introduce the notion of a Chemical Superhyperstructure and examine its foundational properties. We further extend the idea of a Weak Chemical Hyperstructure by defining the Weak Chemical Superhyperstructure via the Weak Superhyperstructure (SHv-Structure) framework, and provide an overview of its behavior. These constructions offer a concise and flexible means to represent hierarchical relationships in chemical systems.
