  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.
