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Characterization of weighted complex networks.

To account for possible distinct functional roles played by different nodes and links in complex networks, we introduce and analyze a class of weighted scale-free networks. The weight of a node is assigned as a random number, based on which the weights of links are defined. We utilize the concept of betweenness to characterize the weighted networks and obtain the scaling laws governing the betweenness as functions both of the weight and of the degree. The scaling results may be useful for identifying influential nodes in terms of physical functions in complex networks.