History
The Wiener index is named after Harry Wiener, who introduced it in 1947; at the time, Wiener called it the "path number". It is the oldest topological index related to molecular branching. Based on its success, many other topological indexes of chemical graphs, based on information in the distance matrix of the graph, have been developed subsequently to Wiener's work.
The same quantity has also been studied in pure mathematics, under various names including the gross status, the distance of a graph, and the transmission. The Wiener index is also closely related to the closeness centrality of a vertex in a graph, a quantity inversely proportional to the sum of all distances between the given vertex and all other vertices that has been frequently used in sociometry and the theory of social networks.
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