PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Use of the Szeged index and the revised Szeged index for measuring network bipartivity
Tomaž Pisanski and Milan Randić
Discrete appl. math. Volume 158, Number 17, pp. 1936-1944, 2010. ISSN 0166-218X

Abstract

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.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:8277
Deposited By:Boris Horvat
Deposited On:21 February 2012