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Weighted competition scale-free network.

While many scale-free (SF) networks have been introduced recently for complex systems, most of them are binary random graphs and the rate at which the node in the network increases its connectivity depends on the time it arrived. We propose a model of weighted scale-free networks incorporating a fit-gets-richer scheme which means the connectivity of the node depends on both the degree and fitness of the node. The topology and weights of links of the network evolve as time goes on. The combined numerical and analytical approach indicates that asymptotically the scaling behaviors of the total weight distribution and the connectivity distribution are identical. The asymptotical sameness has also been observed in real networks.