The Modified Wiener Matrices

The modified edge-Wiener matrix, denoted by is defined as (NikoliiS et al., 2001b) 

Consequently, the modified edge-Wiener matrix can be directly obtained from the edge-Wiener matrix W for the nonvanishing matrix elements  

Summation of nonzero elements in the upper or lower matrix-triangle gives the modified edge-Wiener index. 

A generalization of the modified Wiener matrix leading to a class of modified Wiener indices has also been proposed (Gutman et al 2004). 

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