Topological indices: their nature, mutual relatedness, and applications

AbstractDuring the last two decades a large number of numerical graph invariants (topological indices) have been defined and used for correlation analysis in theoretical chemistry, pharmacology, toxicology, and environmental chemistry. However, no systematic study has been undertaken to determine to what extent these indices are correlated with each other. In the present paper we have carried out a principal component analysis (PCA) of 90 topological parameters derived from 3692 distinct chemicals taken from an environmental database consisting of nearly nineteen thousand compounds. The PCA using the correlation matrix resulted in 10 principal components (PC's) with eigenvalues greater than 1. These ten PC's explained over 92% of the variance in the standardized data. The first four PC's explained over 78% of the variance and the interpretations of these four PC's is given in terms of the chemical structures at the extremes of these PC's