Wiener index
Encyclopedia
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 Harry Wiener in 1947. 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.
Wiener index is the oldest topological index related to molecular branching. 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. Also, different modifications of Wiener index were introduced (for example, Extended Wiener index).
Chemical graph theory
Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena....
, the Wiener index (also Wiener number) is a topological index
Topological index
In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index also known as a connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters...
of a molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
, defined as the sum of the numbers of edges in the shortest paths in a chemical graph between all pairs of non-hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
atoms in a molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
. It was introduced by Harry Wiener in 1947. Wiener index may be calculated using the Floyd–Warshall algorithm. Bojan Mohar and Tomaž Pisanski
Tomaž Pisanski
Tomaž Pisanski is a Slovenian mathematician working mainly in graph theory.In 1980 he calculated the genus of the Cartesian product of any pair of connected, bipartite, d-valent graphs using a method that was later called the White-Pisanski method.In 1982 Vladimir Batagelj and Pisanski proved...
presented an efficient algorithm for computing the Wiener index of a tree.
Wiener index is the oldest topological index related to molecular branching. 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. Also, different modifications of Wiener index were introduced (for example, Extended Wiener index).