Novel eigenvector centrality indices for octane isomers to explore their physicochemical properties.

In chemical graph theory, a molecular structure is represented as a molecular graph [Formula: see text], where [Formula: see text] denotes the non-empty set of atoms (vertices) and [Formula: see text] represents the set of bonds (edges) between the atoms. Centrality measures in a molecular graph are vital for understanding the importance of individual atoms. Among various centrality measures, the eigenvector centrality is a robust metric that captures both the quantity and quality of connections to identify the most influential atoms. Mathematically, the eigenvector centrality [Formula: see text] of an atom [Formula: see text] in [Formula: see text] can be defined as the [Formula: see text] entry in the normalized eigenvector corresponding to the largest eigenvalue [Formula: see text] of the adjacency matrix [Formula: see text], where [Formula: see text] if an atom [Formula: see text] is adjacent to an atom [Formula: see text] and [Formula: see text] otherwise. That is, [Formula: see text] where [Formula: see text] is the number of atoms in [Formula: see text]. In this paper, seven eigenvector centrality-based topological indices are introduced and applied to octane isomers. These indices are utilized in QSPR (Quantitative Structure-Property Relationship) analysis to investigate the properties such as density, mean radius, entropy and more. The results establish a statistically significant and strong correlation between the computed indices and properties of octane isomers. The reliability and accuracy of the regression models are further confirmed through Y-randomization and chi-square goodness-of-fit tests, highlighting the potential of these indices for applications in cheminformatics-based predictive modeling.