Topological and topographical indices

The number of topological and topographical indices increases each month, with recent additions including new shape descriptors [59], descriptors based on graph valence shells [60], and a descriptor based on topological distance counts [61], The latter is shown to be easier to compute while giving results at least as good as the CoMFA and EVA descriptors mentioned below. 

In QSAR and QSPR studies, the standard ways of removing redundancy from large numbers of topological and topographical indices include principal component analysis, chi-squared analysis, and multiple regression analysis (MRA). Most QSAR and QSPR applications deal with very small datasets, and so the dimensionality does not cause a problem for PCA or chi-squared analysis. MRA does not impose any restrictions on the type and number of descriptors. The selection process is based on two principles, namely, to cover as much of parametric space as possible (principle of variance) while choosing independent descriptors (principle of orthogonality). 

Topological and topographical indices In QSP/AR, this class of descriptors is extensively used by chemists. Extensive literature on the subject exists, and many novel indices are still being introduced. Among the classic ones, the Wiener index is best known.This index is... 

A search for extrema in — V2p reveals maxima in the VSCCs that can be ascribed to bonded and nonbonded electron pairs. The different and distinctive properties of sulfides and oxides are examined in terms of the number and the positions of the electron pairs and the topographic features of the Laplacian maps. The evidence provided by p and its topological properties indicates that the bonded interactions in sulfides are more directional, for a given M-cation, than in oxides. The value and the length of a given M-S bond are reliable measures of a bonded interaction the greater the accumulation of p and the shorter the bond, the greater its shared (covalent) interaction. 

---