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September 19, 2025Open Access

Three-Dimensional or Multi-Dimensional Molecular Hyperstructure and Molecular HyperGraph

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This work demonstrates intrinsic geometric properties of hyperstructures in molecular chemistry, suggesting a new modeling approach.

Hyperstructures, demonstrated through chemical examples, provide a way to represent complex molecular models with explicit numerical coordinates.
The framework's definitions of geometry-aware configurations allow for the intrinsic representation of bond lengths, angles, and torsions.
A canonical lifting scheme ensures consistent embeddings for hyperedges and superedges, which enhances the understanding of molecular arrangements.
Reduction theorems indicate that complex structures can simplify to molecular graphs, promoting usability within classical cheminformatics.

Takaaki Fujita (2025) studied this question.

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September 19, 2025Open Access

View Full Paper

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Authors

This work demonstrates intrinsic geometric properties of hyperstructures in molecular chemistry, suggesting a new modeling approach.

Hyperstructures, demonstrated through chemical examples, provide a way to represent complex molecular models with explicit numerical coordinates.
The framework's definitions of geometry-aware configurations allow for the intrinsic representation of bond lengths, angles, and torsions.
A canonical lifting scheme ensures consistent embeddings for hyperedges and superedges, which enhances the understanding of molecular arrangements.
Reduction theorems indicate that complex structures can simplify to molecular graphs, promoting usability within classical cheminformatics.

Takaaki Fujita (2025) studied this question.

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