Weighted scale-free networks with variable power-law exponents

We present a weighted scale-free network model, in which the power-law exponents can be controlled by the model parameters. The network is generated through the weight-driven preferential attachment of new nodes to existing nodes and the growth of the weights of existing links. The simplicity of the model enables us to derive analytically the various statistical properties, such as the distributions of degree, strength, and weight, the degree–strength and degree–weight relationship, and the dependencies of these power-law exponents on the model parameters. Finally, we demonstrate that networks of words, coauthorship of researchers, and collaboration of actor/actresses are quantitatively well described by this model.