2004/08/12 by Tibor Antal, T. Antal, P. L. Krapivsky · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Graph theory and applications #Opinion Dynamics and Social Influence #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.71.026103
published as Phys. Rev. E 71, 026103 (2005) · 6 pages, 2 eps figures
arxiv created 2004/08/12 · openalex publication_date 2005/02/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.