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Evolving networks with disadvantaged long-range connections.

R Xulvi-Brunet1, I M Sokolov

  • 1Institut für Physik, Humboldt Universität zu Berlin, Invalidenstrasse 110, D-10115 Berlin, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
Summary

This study introduces a network growth model where long-range connections are penalized. The network structure transitions from scale-free to stretched exponential as the penalty parameter increases, while preserving small-world properties.

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Area of Science:

  • Network Science
  • Complex Systems
  • Statistical Physics

Background:

  • Scale-free networks, characterized by power-law degree distributions, are common in nature.
  • Preferential attachment is a key mechanism for generating scale-free networks.
  • Understanding deviations from pure scale-free behavior is crucial for modeling real-world systems.

Purpose of the Study:

  • To investigate the impact of distance-dependent connection probability on growing networks.
  • To analyze how a tunable parameter (alpha) influences network topology and properties.
  • To determine the transition point where network characteristics deviate from scale-free models.

Main Methods:

  • Simulating network growth with a modified preferential attachment rule.

Related Experiment Videos

  • Introducing a probability of connection proportional to d(-alpha), where d is distance.
  • Analyzing node degree distributions and small-world properties across different alpha values.

    • Main Results:

    • Networks with alpha<1 exhibit properties similar to traditional scale-free networks.
    • For alpha>1, the node degree distribution shifts from a power law to a stretched exponential.
    • The small-world property remains robust across all tested values of alpha.

    Conclusions:

    • The model demonstrates a tunable transition between scale-free and non-scale-free network regimes.
    • Network structure is sensitive to the balance between local and long-range attachment probabilities.
    • The preserved small-world property suggests resilience in network connectivity despite changes in degree distribution.