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Scale-free networks emerging from weighted random graphs.

Tomer Kalisky1, Sameet Sreenivasan, Lidia A Braunstein

  • 1Minerva Center and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel. kaliskt@mail.biu.ac.il

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 12, 2006
PubMed
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Erdös-Rényi random graphs form scale-free supernode networks when nodes in percolation clusters merge. This emergent scale-free structure (lambda=2.5) may explain real-world network evolution.

Area of Science:

  • Network Science
  • Statistical Physics
  • Graph Theory

Background:

  • Erdös-Rényi random graphs are fundamental models in network science.
  • Understanding emergent properties like scale-invariance is crucial for complex systems.
  • Percolation theory describes the formation of connected clusters in random networks.

Purpose of the Study:

  • To investigate the structural properties of supernode networks derived from weighted random graphs.
  • To determine if these supernode networks exhibit scale-free characteristics.
  • To explore the implications for minimum spanning trees and real-world network formation.

Main Methods:

  • Generating Erdös-Rényi random graphs with random link weights.
  • Defining and constructing a supernode network by merging nodes within percolation clusters below a threshold.

Related Experiment Videos

  • Analyzing the degree distribution of the resulting supernode network to assess scale-invariance.

    • Main Results:

    • The generated supernode network exhibits a scale-free degree distribution, P(k) ~ k^(-lambda), with lambda = 2.5.
    • The minimum spanning tree within these random graphs is composed of percolation clusters.
    • These clusters are interconnected, forming a scale-free tree structure with lambda = 2.5.

    Conclusions:

    • The spontaneous emergence of a percolation threshold leads to naturally occurring scale-free supernode networks.
    • This phenomenon provides a potential mechanism for the evolution of scale-free networks observed in nature.
    • The findings offer insights into the interplay between random processes, optimization, and network structure.