On the redundancy of topological indices

Topological indices are molecular descriptors based on the graph of a molecule. Numerous topological indices, including the popular connectivity index or the Zagreb indices, have been proposed, many of these were found to be strongly correlated. This is a serious problem for QSAR/QSPR studies as data processing may give meaningless results or fail completely. Using random graphs as a mathematical model for molecular graphs, Hollas shows that certain topological indices are necessarily correlated. This correlation can be arbitrarily close to a perfect linear relationship, in which the information provided by either index is completely redundant. The underlying reasons are identified and simple transformations of the considered topological indices are proposed, reducing or eliminating unwanted correlations. Hollas also shows that the variance of certain topological indices depends on the number of atoms and how a uniform variance throughtout the data set can be obtained. Experimental results with chemical graphs support these findings, which are of practical importance for QSAR/ QSPR studies and other applications of topological indices. The author, Boris Hollas, studied mathematics and computer science at Gießen University. He works as a research assistant at the departement of theoretical computer science at Ulm University.