Weight-driven growing networks

Abstract

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.

6 pages, 2 eps figures

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• Condensation transitions in a model for a directed network with weighted links
• Effects of accelerating growth on the evolution of weighted complex networks
• Recursive weighted treelike networks
• Statistics of Weighted Networks
• Construction of bipartite and unipartite weighted networks from collections of journal papers
• Weighted hypersoft configuration model
• Complex Networks: Time-Dependent Connections and Silent Nodes
• Weighted networks of scientific communication: the measurement and geometrical role of weight
• Analytic Solution to Clustering Coefficients on Weighted Networks
• A Survey of Evolving Models for Weighted Complex Networks based on their Dynamics and Evolution
• An egonet-based approach to effective weighted network comparison
• Evolving Model of Weighted Networks Inspired by Scientific Collaboration Networks