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) approximately 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.
Antal
T
T
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Krapivsky
P L
PL
D000222:Adaptation, Physiological / Q000502:physiology*; D000818:Animals; D002468:Cell Physiological Phenomena; D049109:Cell Proliferation; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D009415:Nerve Net / Q000254:growth & development*; D009473:Neuronal Plasticity / Q000502:physiology; D011158:Population Growth; D015398:Signal Transduction / Q000502:physiology*