Weight-driven growing networks

We study growing networks in which each link carries a certain weight (randomly assigned at birth and fixed thereafter). The weight of a node is defined as the sum of the weights of the links attached to the node, and the network grows via the simplest weight-driven rule: A newly added node is connected to an already existing node with the probability which is proportional to the weight of that node. We show that the node weight distribution n(w) has a universal tail, that is, it is independent of the link weight distribution: n(w)similar to w(-3) as w ->infinity. Results are particularly neat for the exponential link weight distribution when n(w) is algebraic over the entire weight range.