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

Azzam Altairi1, Zaied Alhaj2,3, Mohammed Alsharafi4,5,6

  • 1Department of Biomedical Engineering, Institute of Graduate Studies, Istanbul University - Cerrahpasa, Istanbul, Turkey.

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|February 21, 2026
PubMed
Summary

We introduce novel modified bond-based graph descriptors that combine vertex and bond information for improved chemoinformatics modeling. These new descriptors show enhanced predictive power in quantitative structure-activity relationship (QSAR) studies.

Keywords:
AntibacterialDrug discoveryModified bond-based indicesMolecular graph theoryPhysicochemical propertiesQSARQSPR

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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.