Data-driven analysis of chemical graph of carbazole and diketopyrrolopyrrole

Topological indices play a key role in molecular graph theory, consisting of mathematical tools that allocate numerical values to molecular structures. These indices are used to anticipate a variety of physicochemical, biological, and pharmacological properties of chemical compounds. This study performs a detailed statistical analysis of different topological indices, such as the First Zagreb index, scrutinizing its associations with other indices through regression modeling and correlation analysis. Research generates predictive models, including linear, quadratic, and cubic regression equations by using machine learning techniques. The results show that linear regression delivers the most accurate predictions, whereas the quadratic regression model improves the understanding of actual versus predicted values, improving the valuation of molecular properties. A using statistical evaluation of the selected topological indices involved computing essential metrics such as mean, median, variance, standard deviation, range, interquartile range (IQR), skewness, and kurtosis. These metrics expand our understanding of the allocation and adaptability of indices, confirming their robustness in molecular description and predictive modeling. Using a machine learning-based statistical method, the study increases the use of topological indices in cheminformatics, drug discovery, and materials science. These findings assistance the development of QSAR and QSPR models, supporting the critical role of statistical verification in molecular descriptor. This method promotes more accurate, data-driven strategies in computational chemistry and bioinformatics.