Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 375452, 16 pages
Statistical Analysis of Weighted Networks
Mathematics Department, Aristotle University, 54124 Thessaloniki, Greece
Received 16 May 2007; Accepted 1 February 2008
Academic Editor: Francisco Solis
Copyright © 2008 I. E. Antoniou and E. T. Tsompa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely, average path length, degree distribution, and clustering coefficient. Although the degree distribution and the average path length admit straightforward generalizations, for the clustering coefficient several different definitions have been proposed in the literature. We examined the different definitions and identified the similarities and differences between them. In order to elucidate the significance of different definitions of the weighted clustering coefficient, we studied their dependence on the weights of the connections. For this purpose, we introduce the relative perturbation norm of the weights as an index to assess the weight distribution. This study revealed new interesting statistical regularities in terms of the relative perturbation norm useful for the statistical characterization of weighted graphs.