  Many biological, ecological and economic systems are best described by
weighted networks, as the nodes interact with each other with varying strength.
However, most network models studied so far are binary, the link strength being
either 0 or 1. In this paper we introduce and investigate the scaling
properties of a class of models which assign weights to the links as the
network evolves. The combined numerical and analytical approach indicates that
asymptotically the total weight distribution converges to the scaling behavior
of the connectivity distribution, but this convergence is hampered by strong
logarithmic corrections.
