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, that is independent on the link weight distribution, tail: n(w) ~ w^-3 as w->oo. Results are particularly neat for the exponential link weight distribution when n(w) is algebraic over the entire weight range.