Relations frequency hypermatrices in mutual, conditional and joint entropy-based information indices

Area of Science:

• Computational Chemistry
• Cheminformatics
• Mathematical Chemistry

Background:

• Graph-theoretic matrix representations are crucial for topological molecular descriptors (MDs).
• A novel duplex relations frequency matrix (F) and derived information indices (IFIs) were previously introduced.
• Existing methods rely on incidence matrix generalizations for molecular graph analysis.

Purpose of the Study:

• To introduce and explore hypermatrices in graph-theoretic chemistry.
• To generalize existing information indices (IFIs) using hypermatrix representations.
• To evaluate the enhanced predictive capacity of these new descriptors in QSPR studies.

Main Methods:

• Development of triple and quadruple relations frequency matrices based on hypermatrix concepts.
• Redefinition of mutual, conditional, and joint entropy-based IFIs using hypermatrices.
• Implementation of these generalized IFIs in the GT-STAF module of the TOMOCOMD-CARDD program.

Main Results:

• Hypermatrix-based IFIs demonstrate enhanced entropy and variability, particularly conditional and mutual entropy-based ones.
• Regression models for partition coefficient (Log P) and specific rate constant (Log K) showed improved statistical parameters.
• The new hypermatrix approach outperformed existing methods for predicting physicochemical properties of 2-furylethylene derivatives.

Conclusions:

• Hypermatrix representations offer a powerful extension to graph-theoretic molecular descriptors.
• The generalized IFIs exhibit superior performance in Quantitative Structure-Property Relationship (QSPR) studies.
• This approach provides valuable tools for molecular modeling, diversity analysis, and drug discovery.