Molecular graphs edge-weighted

From vertex-weighted molecular graphs, edge weights can be derived from some combination of the weights of the two vertices incident to the edge ... 

For vertex- and edge-weighted molecular graphs, the weighted distance matrix is generally defined as a square symmetric A x A matrix, A being the number of graph vertices. 

Ivanduc, 0., Ivanciuc, T., Balahan, A. T. Vertex- and edge-weighted molecular graphs and derived structural descriptors. In Topological Indices and Related Descriptors in QSAR and QSPR, Devillers, J. Balahan, A. T. (eds.), Gordon ... 

A molecular weighted path number obtained by weighting graph edges with -> conventional bond order [Randic and Jurs, 1989] ... 

Plavsic, D, Soskic, M., Dakovic, Z., Gutman, I. and Graovac, A. (1997). Extension of the Z Matrix to Cycle-Containing and Edge-Weighted Molecular Graphs. J.Chem.InfComputSci., 37,529-534. 

These are molecular descriptors calculated from the H-depleted molecular graph by analogy with the —> hyper-Wiener index. The general formula, called by Ivanciuc hyper-Wiener operator [Ivanciuc, Ivanciuc et al., 1997 Ivanciuc, 2001c], to calculate hyper-Wiener-type indices from vertex- and/or edge-weighted molecular graphs is... 

Moreover, matrices can be derived from unweighted or vertex- and/or edge-weighted molecular graphs in the latter case, several weighted matrices can be obtained depending on the —> weighting scheme. 

An example of a reduced graph is a molecular graph composed of weighted edges and with vertex number equal to the number of functional groups perceived by using predefined rules [Takahashi, Sukekawa et al., 1992]. 

The weighted electronic connectivity matrix (or CEP matrix) of an edge-weighted molecular graph is a symmetric weighted adjacency matrix, of size A x A, whose elements are defined as [Berinde and Berinde, 2004]... 

Weighting schemes for graph vertices and edges are used to encode in a numerical form information about atom and bond properties that are not represented in a simple molecular graph. 

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