From graph theory to chemoinformatics: modified bond-based indices and a hypothesis-driven multi-task QSAR/QSPR...

Area of Science:

• Chemoinformatics and Cheminformatics
• Mathematical Chemistry
• Graph Theory

Background:

• Classical graph-theoretic degree-based descriptors are crucial in chemoinformatics and QSPR/QSAR, but often focus solely on vertex degrees or multiplicative bond contributions.
• Existing methods lack a unified approach to integrate both vertex and bond information effectively, limiting their descriptive and predictive capabilities.

Purpose of the Study:

• To introduce and systematically study a new family of modified bond-based graph descriptors.
• To develop a flexible and analytically tractable framework for these descriptors, suitable for machine learning applications in chemoinformatics.

Main Methods:

• Introduced modified bond-based indices weighting edges with local bond factors and vertex kernels.
• Developed a unified edge-partition representation for symmetric kernels, expressing indices as sums over degree classes.
• Derived closed-form expressions for sixteen modified indices on various benchmark graph families (paths, cycles, complete graphs, etc.).
• Obtained sharp degree-extreme bounds for a subset of indices, characterizing equality in regular graphs.

Main Results:

• Presented a novel family of sixteen modified bond-based graph descriptors.
• Derived analytical expressions for these descriptors across diverse graph structures, revealing asymptotic growth patterns and extremal properties.
• Demonstrated the superior predictive utility of these descriptors in a large multi-task QSAR/QSPR pipeline on antibacterial molecules, outperforming physicochemical descriptors.

Conclusions:

• The proposed modified bond-based descriptors offer a flexible and analytically tractable way to couple vertex and bond information.
• These descriptors are well-suited as structured features for modern chemoinformatics and graph-based machine learning models.
• The enhanced predictive performance in QSAR/QSPR studies validates their utility for modeling molecular properties.