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Coordination sequences and information spreading in small-world networks.

Carlos P Herrero1

  • 1Instituto de Ciencia de Materiales, Consejo Superior de Investigaciones Científicas (CSIC), Campus de Cantoblanco, 28049 Madrid, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 22, 2002
PubMed
Summary

We investigated information spread in small-world networks across dimensions 1-3. Our findings reveal how network disorder and active site fraction dictate information propagation, distinguishing between whole-system spread and localized confinement.

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Area of Science:

  • Complex Networks
  • Information Theory
  • Statistical Physics

Background:

  • Small-world networks exhibit unique topological properties.
  • Understanding information diffusion is crucial in various scientific domains.

Purpose of the Study:

  • To analyze information spread in d-dimensional small-world networks (d=1, 2, 3).
  • To investigate the influence of network dimension and disorder on information propagation dynamics.

Main Methods:

  • Numerical simulations of coordination sequences in generated small-world networks.
  • Modeling information spreading with a fraction of active network sites.
  • Analysis of asymptotic behaviors and propagation regimes.

Main Results:

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  • Coordination sequence C(n) shows asymptotic behavior dependent on dimension (d) and rewiring probability (p).
  • Information spread is characterized by lambda, influenced by p, active site fraction (q), and d.
  • Two distinct spreading regimes identified: whole-system propagation (lambda>1) and damped, confined spread (lambda<1).

Conclusions:

  • The study establishes a quantitative relationship between network topology, disorder, and information diffusion.
  • Results offer insights into site percolation phenomena within small-world networks.
  • Findings are relevant for understanding complex system dynamics and emergent behaviors.