Phase transition in the link weight structure of networks

Piet Van Mieghem and Serena M. Magdalena
Phys. Rev. E 72, 056138 – Published 30 November 2005

Abstract

When transport in networks follows the shortest paths, the link weights are shown to play a crucial role. If the underlying topology with N nodes is not changed and if the link weights are independent from each other, then we show that, by tuning the link weights, a phase transition occurs around a critical extreme value index αc of the link weight distribution. If the extreme value index of the link weight distribution α>αc, transport in the network traverses many links whereas for α<αc, all transport flows over a critical backbone consisting of N1 links. For connected Erdös-Rényi random graphs Gp(N) and square lattices, we have characterised the phase transition and found that αcbNβ with βGp(N)0.63 and βlattice0.62.

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  • Received 10 March 2005

DOI:https://doi.org/10.1103/PhysRevE.72.056138

©2005 American Physical Society

Authors & Affiliations

Piet Van Mieghem and Serena M. Magdalena

  • Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands

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Issue

Vol. 72, Iss. 5 — November 2005

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