Edge-Connectivity Indices in QSPR/QSAR Studies. 1. Comparison to Other Topological Indices in QSPR Studies

Abstract

The linear independence of the edge-connectivity index to other first-, second-, and third-generation topological indices is demonstrated by using principal component analysis for octane isomers. Most of the topological indices are loaded in one factor, while the edge connectivity is loaded in another independent factor. The edge-connectivity index does not produce linear correlations (R ≤ 0.7) with any of the almost 40 topological indices studied. This index produced the best single-variable quantitative structure−property relationship (QSPR) models for five of the seven physicochemical properties of octanes studied. It is concluded that the edge connectivity is an independent index containing important structural information to be used in QSPR/QSAR (QSAR = quantitative structure−activity relationship) studies.

Applying pattern recognition methods plus quantum and physico‐chemical molecular descriptors to analyze the anabolic activity of structurally diverse steroids

“…39,40, [43][44][45] Finally, some of the most important conclusions, which could can be drawn from a factor analysis that will be of large usefulness in the present article are the following 39,40,43-45 : (1) variables with a high loading in the same factor are interrelated and will be the more, the higher the loadings, (2) no correlation exists between variables having nonzero loadings only in different factors. These are the principal ideas that permit the interpretation of the factorial structure, obtained using the factorial analysis as a classification method, and (3) only variables with high loadings in different factors may be combined in a regression equation to eliminate collinearities.…”

“…The theoretical aspects of this statistical technique have been extensively exposed in the literature including many chemical applications. [39][40][41][42][43][44][45] The main uses of factorial analytical techniques are: (1) to reduce the number of variables, and (2) to detect structure in the relationships between variables, namely, to classify variables 44,46 In this approach, factorial loadings (or ''new'' variables) are obtained from original variables (quantum and physicochemical MDs). Thus, these factors capture all the ''essence'' of these MDs, because they are linear combinations of the original items.…”

“…39,40,[43][44][45] Factorial loadings from the principal component analysis, after a varimax normalized rotation of the first twelve factors, are shown in Table1. Furthermore, the results of the factorial analysis performed here are summarized in Table2.…”

Degree-Based Topological Indices

“…[199][200][201][202] When instead of the molecular graph G its line graph L(G) is used, then instead of the ordinary Randić index one arrives at Estrada's "edge connectivity index" [203][204][205] A comparison between Randić and edgeconnectivity indices of benzenoid hydrocarbons was reported. 206 In the case of Zagreb indices, the transformation G → L(G) yields the "reformulated Zagreb indices".…”

Bond-based global and local (bond, group and bond-type) quadratic indices and their applications to computer-aided molecular design. 1. QSPR studies of diverse sets of organic chemicals

“…The use of octane isomers as a very suitable data set for testing TIs has been advocated by Randić and Trinajstić [53,54]. In fact, this dataset has been used by several researchers to evaluate the modeling power of their new MDs [2, 11,55,56]. This selection is recommended due to the fact that most of the physicochemical properties commonly studied in QSPR analyses with TIs are interrelated for data sets of compounds with different molecular weights, for instance for alkanes with two to nine carbon atoms.…”