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Related Concept Videos

Weighted Mean00:57

Weighted Mean

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Related Experiment Videos

Voter models on weighted networks.

Andrea Baronchelli1, Claudio Castellano, Romualdo Pastor-Satorras

  • 1Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 30, 2011
PubMed
Summary
This summary is machine-generated.

This study investigates voter and Moran processes on weighted complex networks. We found consensus time depends on edge weights and degree distribution, revealing diverse scaling laws.

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Area of Science:

  • Statistical Physics
  • Network Science
  • Computational Social Science

Background:

  • The voter model and Moran process are fundamental models for opinion dynamics and evolutionary game theory.
  • Complex networks exhibit diverse structures influencing emergent phenomena.
  • Edge weights in networks can represent interaction strength or influence, significantly altering dynamics.

Purpose of the Study:

  • To analyze the voter and Moran processes on complex networks with degree-dependent edge weights.
  • To develop a theoretical framework for understanding consensus formation in such systems.
  • To identify phase diagrams and scaling laws governing consensus times.

Main Methods:

  • Heterogeneous mean-field theory to derive conservation laws and calculate exit probabilities.
  • Analytical treatment using heterogeneous pair approximation.
  • Numerical simulations to validate theoretical predictions.

Main Results:

  • A detailed phase diagram for consensus time was derived based on weight exponent θ and degree distribution exponent γ.
  • Various scaling laws for consensus time were identified, dependent on θ and γ.
  • Good agreement between theoretical predictions and numerical simulations was observed for small |θ|.

Conclusions:

  • The heterogeneous mean-field approach effectively captures key aspects of voter and Moran dynamics on weighted networks.
  • Edge weight properties significantly influence consensus times and exhibit complex scaling behaviors.
  • Further theoretical work is needed to fully understand dynamics for large |θ|.