  We develop a simple theoretical framework for the evolution of weighted
networks that is consistent with a number of stylized features of real-world
data. In our framework, the Barabasi-Albert model of network evolution is
extended by assuming that link weights evolve according to a geometric Brownian
motion. Our model is verified by means of simulations and real world trade
data. We show that the model correctly predicts the intensity and growth
distribution of links, the size-variance relationships of the growth of link
weights, the relationship between the degree and strength of nodes, as well as
the scale-free structure of the network.
