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Related Experiment Video

Updated: Jul 4, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Local leaders in random networks.

Vincent D Blondel1, Jean-Loup Guillaume, Julien M Hendrickx

  • 1Department of Mathematical Engineering, Université catholique de Louvain, Louvain-la-Neuve, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary

In random networks, we identified local leaders, nodes with the highest degree among neighbors. A critical transition occurs at a degree distribution exponent of 3, determining if high-degree nodes become leaders.

Related Experiment Videos

Last Updated: Jul 4, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Area of Science:

  • Network Science
  • Statistical Physics

Background:

  • Local leaders are nodes with degrees exceeding all neighbors.
  • Understanding leader emergence is key in network analysis.

Purpose of the Study:

  • Derive an analytical expression for local leader probability.
  • Investigate the role of degree distribution in leader emergence.

Main Methods:

  • Analytical calculations for leader probability.
  • Computer simulations to verify theoretical findings.
  • Analysis of finite-size effects.

Main Results:

  • An analytical formula for the probability of a node of degree k being a local leader was derived.
  • A phase transition was identified at a power-law exponent of gamma(c)=3.
  • High-degree nodes transition from being leaders to non-leaders based on this exponent.

Conclusions:

  • The study provides a theoretical framework for understanding local leadership in networks.
  • Degree distribution tail behavior critically influences leader identification.
  • Finite-size effects are important for accurate simulation results.