Power-law strength-connectivity dependence in weighted scale-free network
Abstract
We present a simple model of weighted network showing a possible non linear behavior of the scaling of the strength of a node with its connectivity. The model is susceptible of a number of modifications. A relevant one that we call weighted fitness network is considered here. This model can undergo a structural phase transition between a first phase where all links have an infinitesimal fraction of the total weight of the network and a second phase where there are few links with a finite fraction of the total weight of the network. We identify the point where this transition occurs as a function of the ratio between the rate at which the connections increase and the rate at which the weights are strengthened.Keywords
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