Use of the Szeged index and the revised Szeged index for measuring network bipartivity

We have revisited the Szeged index (Sz) and the revised Szeged Index (Sz*), both of which represent a generalization of the Wiener number to cyclic structures Unexpectedly we found that the quotient of the two indices offers a novel measure for characterization of the degree of bipartivity of networks, that is, offers a measure of the departure of a network, or a graph, from bipartite networks or bipartite graphs, respectively. This is because the two indices assume the same values for bipartite graphs and different values for non-bipartite graphs We have proposed therefore the quotient Sz/Sz* as a measure of bipartivity In this note we report on some properties of the revised Szeged index and the quotient Sz/Sz* Illustrated on a number of smaller graphs as models of networks. (C) 2010 Elsevier B.V. All rights reserved.