Harary index

Harary Index The Harary index, H, is defined as the sum of the squares of the reciprocal nonzero distances in D [6,7]  

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Table 5.2 Bond Contributions of the Individual Bonds in 2,3-Dimethylhexane for Calculation of Harary Index... 

Figure 5.6 Bond distribution of Harary index (H) for 2,3-dimethylhexane.

The Harary index H (also called Harary number) is a molecular topological index [Ivanciuc et al, 1993b Plavsic et al, 1993b] derived from the -> reciprocal distance matrix D- by the Wiener operator YF ... 

The Harary index increases with both molecular size and - molecular branching, it is therefore a measure of molecular compactness like the - Wiener index. However, the Harary index seems to be a more discriminating index than the Wiener index. 

The Harary index and hyper-Harary index, defined only for acyclic graphs, are obtained from, respectively, the P -order sparse -> reciprocal Wiener matrix W ... 

Harary number Harary index -> Harary indices... 

Moreover, a number of topological indices have been expressed as functions of the Wiener index or as its extensions [Zhu et ai, 1996b] examples are - detour/Wiener index, - hyper-Wiener index, -> Harary index, - total information content on the distance magnitude, mean information content on the distance magnitude, and - mean information content on the distance degree magnitude. 

Plavsic, D., Nikolic, S., Trinajstic, N. and Mihalic, Z. (1993b). On the Harary Index for the Characterization of Chemical Graphs. J.Math.Chem., 12,235-250. 

For 2, = 1, this index coincides with twice the Harary index and for 2, = 2 with twice the Harary number (see below). 

Wis the Wiener index, W the average Wiener index, H the Harary index, H the Harary number, RDCHI the RDCHI index, and RDSQthe J DSQ index. 

The Harary index H [Plavsic, Nikolic et al., 1993b], also called RDSUMindex [Ivanciuc, Balaban et al., 1993b], is a molecular topological index derived from the reciprocal distance matrix by the Wiener operator Wi ... 

Reciprocal distance matrix D and Harary index H for 2-methylpentane. 

The index Q increases with the molecule size and branching, whereas index S increases with size but decreases with branching index D increases with cyclicity and decreases with branching. For acyclic graphs, index A is the Harary index (denoted as H by Trinajstic and RDS UMhy Balaban). Finally, index P increases with size and decreases with branching for hydrocarbons, this index shows the minimum number of degeneracies with respect to the other path count-based indices. 

The edge-Harary index is defined as the half sum of the elements of the edge-weighted Harary matrix ... 

Of course, for A, = 1, Wj is the Wiener index, for A, = — 1, the Harary index (or RDS UM index), and for A, = —2 the Harary number. Other X values, namely, 2, = 1/3 and 2,= —1/3, were used to model boiling points of C8 alkane isomers [Lucic, Milicevic et al., 2003], Note that for positive integer X values, W). indices coincide with the distance distribution moments Dx [Klein and Gutman, 1999]. 

Harary index — twelve years later. Croat. Chem. Acta, 75, 847—868. 

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