In chemical graph theory, the Wiener index (also Wiener number) is a topological index of a molecule, defined as the sum of the numbers of edges in the shortest paths in a chemical graph between all pairs of non-hydrogen atoms in a molecule. It was introduced by H. Wiener in 1947.^[1] Wiener index may be calculated using the Floyd–Warshall algorithm. Bojan Mohar and Tomaž Pisanski presented an efficient algorithm for computing the Wiener index of a tree.^[2]

Wiener index is the oldest topological index related to molecular branching.^[3] A tentative explanation of the relevance of the Wiener index in research of QSPR and QSAR is that it correlates with the van der Waals surface area of the molecule.^[4] Also, different modifications of Wiener index were introduced (for example, Extended Wiener index^[5]).

[edit] References

1. ^ H. Wiener, "Structural determination of paraffin boiling points", J. Am. Chem. Soc., 1947, 69(1), 17-20.
2. ^ Bojan Mohar, Tomaž Pisanski, "How to compute the Wiener index of a graph" J. Math. Chemistry 2 (1988) pp. 267-277
3. ^ Roberto Todeschini, Viviana Consonni (2000) "Handbook of Molecular Descriptors", Wiley-VCH, ISBN 3527299130
4. ^ Ivan Gutman, T. Körtvélyesi, "Wiener indices and molecular surfaces" Z. Naturforsch. 50a (1995) pp. 669-671
5. ^ S. S. Tratch, M. I. Stankevitch, and N. S. Zefirov, J. Comp. Chem., 1990, 11, 899.

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