Document Type : Research Article
Authors
Department of Mathematics, Statistics, and Computer Science, Semnan University, Semnan 35131-19111, Iran
10.30473/coam.2026.76560.1363
Abstract
This research evaluates the integration of graph-theoretic topological indices (TIs) with machine learning (ML) frameworks to forecast the physicochemical attributes of anxiolytic drugs. By representing molecular structures as graphs, the study extracted TIs to serve as primary features for four distinct predictive algorithms: basic and optimized support vector regression (SVR-Basic and SVR-Tuned), random forest (RF), and linear regression (LR). To address the constraints of a small sample size, the authors utilized Leave-One-Out cross-validation (LOOCV) and bootstrap resampling to ensure robust performance metrics, including confidence intervals and coefficients of variation (CV\%) for stability assessment. The findings indicate that the combination of hyperparameter refinement and rigorous validation significantly elevates the precision and reliability of ML models in chemical property prediction.
Highlights
- Topological and temperature-based molecular descriptors are computed for 15 anti-anxiety drugs using graph-theoretical formalism.
- SVR-Tuned with Grid Search hyperparameter optimization achieves superior predictive accuracy (R² ≈ 0.999) over SVR-Basic, Random Forest, and Linear Regression.
- Recursive Feature Elimination (RFE) identifies the most predictive temperature-based topological indices for each physicochemical property.
- Models successfully generalize to 10 unseen drug compounds, confirming robustness and out-of-sample predictive capability.
- A rigorous error and residual analysis demonstrate that hyperparameter optimization substantially reduces prediction dispersion and enhances stability.
Keywords
Main Subjects
[1] Abubakar, M.S., Aremu, K.O., Aphane, M., Amusa, L.B. (2024). “A QSPR analysis of physical properties of antituberculosis drugs using neighbourhood degree-based topological indices and support vector regression”. Heliyon, 10(7), e28260. https://doi.org/10.1016/j.heliyon.2024.e28260
[2] Breiman, L. (2001). “Random forests”. Machine Learning, 45(1), 5–32. https://doi. org/10.1023/A:1010933404324
[3] Craske, M.G., Stein, M.B., Eley, T.C., Milad, M.R., Holmes, A., Rapee, M. R., Wittchen, H.-U. (2017). “Anxiety disorders”. Nature Reviews Disease Primers, 3, 17024. https: //doi.org/10.1038/nrdp.2017.24
[4] ChemSpider. (2021). “Search and share chemistry”. Royal Society of Chemistry. https: //www.chemspider.com
[5] Fajtlowicz, S. (1988). “On conjectures of Graffiti”. Discrete Mathematics, 72(1–3), 113– 118. https://doi.org/10.1016/0012-365X(88)90199-9
[6] Ghorbani, M., Hosseinzadeh, M.A. (2012). “A new version of Zagreb indices”. Filomat, 26, 93–100. https://doi.org/10.2298/FIL1201093G
[7] Havare, Ö.Ç. (2022). “Quantitative structure analysis of some molecules in drugs used in the treatment of COVID-19 with topological indices”. Polycyclic Aromatic Compounds, 42, 5249–5260. https://doi.org/10.1080/10406638.2021.1934045
[8] Hettema, J.M., Neale, M.C., Kendler, K.S. (2001). “A review and meta-analysis of the genetic epidemiology of anxiety disorders”. American Journal of Psychiatry, 158(10), 1568–1578. https://doi.org/10.1176/appi.ajp.158.10.1568
[9] Huang, L., Wang, Y., Pattabiraman, K., Danesh, P., Siddiqui, M.K., Cancan, M. (2023). “Topological indices and QSPR modeling of new antiviral drugs for cancer treatment”. Polycyclic Aromatic Compounds, 43, 8147–8170. https://doi.org/10.1080/ 10406638.2022.2145320
[10] Kansal, N., Garg, P., Singh, O. (2023). “Temperature-based topological indices and QSPR analysis of COVID-19 drugs”. Polycyclic Aromatic Compounds, 43, 4148–4169. https: //doi.org/10.1080/10406638.2022.2086271
[11] Kosari, S. (2023). “On spectral radius and Zagreb Estrada index of graphs”. Asian-European Journal of Mathematics, 16(10), 2350176. https://doi.org/10.1142/ S1793557123501760
[12] Kosari, S., Dehgardi, N., Khan, A. (2023). “Lower bound on the KG-Sombor index”. Communications in Combinatorics and Optimization, 8(4), 751–757. https://doi.org/10. 22049/CCO.2023.28666.1662
[13] Kulli, V.R. (2019). “Computation of some temperature indices of HC5C5 [p,q] nanotubes”. Annals of Pure and Applied Mathematics, 20(2), 69–74. https://doi.org/10.22457/ apam.639v20n2a4
[14] Kulli, V. (2025). “Computation of inverse sum indeg uphill index and its polynomial of certain graphs”. International Journal of Mathematics and Computer Research, 13(06), 5346–5350. https://doi.org/10.47191/ijmcr/v13i6.10
[15] Kulli, V.R., Pal, M., Samanta, S., Pal, A. (2020). Handbook of Research on Advanced Applications of Graph Theory in Modern Society. IGI Global. https://doi.org/10. 4018/978-1-5225-9380-5.ch015
[16] Mikaeyl Nejad, S. (2025). “Hybrid of CNN and SVM for cancer type prediction”. Control and Optimization in Applied Mathematics, 10(1), 73–89. https://doi.org/10.30473/ coam.2025.72710.1269
[17] Mondal, S., Dey, A., De, N., Pal, A. (2021). “QSPR analysis of some novel neighbourhood degree-based topological descriptors”. Complex & Intelligent Systems, 7, 977–996. https://doi.org/10.1007/s40747-020-00262-0
[18] Murphy, K.P. (2022). Probabilistic Machine Learning: An Introduction. MIT Press. https://probml.github.io/pml-book/book1.html
[19] Narayankar, K.P., Kahsay, A.T., Selvan, D. (2018). “Harmonic temperature index of certain nanostructures”. International Journal of Mathematics Trends and Technology, 56(8), 575–582. https://doi.org/10.14445/22315373/IJMTT-V56P523
[20] Ramezani Tousi, J., Ghods, M. (2023). “Computing K Banhatti and K hyper Banhatti indices of titania nanotubes TiO2[m, n]”. Journal of Information and Optimization Sciences, 44(1), 207–216. https://doi.org/10.47974/JIOS-1130
[21] Ramezani Tousi, J., Ghods, M. (2024). “Investigating Banhatti indices on the molecular graph and the line graph of glass with M-polynomial approach”. Proyecciones (Antofagasta), 43(1), 199–219. https://doi.org/10.22199/issn.0717-6279-5594
[22] Rauf, A., Naeem, M., Ramzan, R., Cham, A. (2024). “Exploring physicochemical characteristics of cyclodextrin through M-polynomial indices”. Scientific Reports, 14, 200. https://doi.org/10.1038/s41598-024-68775-z
[23] Ravi, V., Desikan, K. (2023). “Curvilinear regression analysis of benzenoid hydrocarbons and computation of some reduced reverse degree-based topological indices”. Scientific Reports, 13, 3239. https://doi.org/10.1038/s41598-023-28416-3
[24] Sadati, S., Talebi, A.A. (2023). “A description of connectivity indices in a cubic fuzzy graph with an application”. Journal of Multiple-Valued Logic and Soft Computing, 40(5–6), 541-568. https://www.oldcitypublishing.com/journals/mvlsc-home/mvlsc-issue-contents/mvlsc-volume-40-number-5-6-2023/ mvlsc-40-5-6-p-541-568
[25] Shahabi, M., Rahbarnia, F. (2026). “A metaheuristic and LP-based approach to irregular face coloring in planar graphs”. Control and Optimization in Applied Mathematics و11(1), 141-151. https://doi.org/10.30473/coam.2025.75246.1325
[26] Shi, X., Cai, R., Ramezani Tousi, J., Talebi, A.A. (2024). “Quantitative structure–property relationship analysis in molecular graphs of anticancer drugs”. Mathematics, 12(13), 1953. https://doi.org/10.3390/math12131953
[27] Shi, X., Kosari, S., Ghods, M., Kheirkhahan, N. (2025). “Innovative approaches in QSPR modelling using topological indices for cancer treatments”. PLOS ONE, 20(2), e0317507. https://doi.org/10.1371/journal.pone.0317507
[28] Vapnik, V.N. (1995). The Nature of Statistical Learning Theory. Springer. https://doi. org/10.1007/978-1-4757-2440-0
[29] Zhang, Y., Khalid, A., Siddiqui, M. K., Rehman, H., Ishtiaq, M., Cancan, M. (2023). “On analysis of temperature-based topological indices of COVID-19 drugs”. Polycyclic Aromatic Compounds, 43, 3810–3826. https://doi.org/10.1080/10406638.2022.2080238
[30] Zhang, X., Saif, M. J., Idrees, N., Kanwal, S., Parveen, S., Saeed, F. (2023). “QSPR analysis of drugs for schizophrenia using topological indices”. ACS Omega, 8(44), 41417– 41426. https://doi.org/10.1021/acsomega.3c05000
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