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Percolation transition in a dynamically clustered network.

A Zen1, A Kabakçioğlu, A L Stella

  • 1Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
PubMed
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This study introduces a modified Barabási-Albert model exhibiting percolation transitions with disconnected clusters. Unlike other models, it shows power-law behavior for the order parameter, differing from the Berezinskii-Kosterlitz-Thouless scenario.

Area of Science:

  • Complex networks
  • Statistical physics
  • Network percolation theory

Background:

  • The Barabási-Albert model is a cornerstone for understanding real-world network growth.
  • Percolation phenomena on growing networks are crucial for studying network robustness and function.
  • Existing models often assume connected cluster formation, limiting the study of disconnected states.

Purpose of the Study:

  • To investigate percolation-like phenomena in a generalized Barabási-Albert model allowing disconnected clusters.
  • To precisely locate the transition point using a novel numerical technique.
  • To analyze finite-size scaling properties and compare them with existing models.

Main Methods:

  • Modification of the Barabási-Albert model's growth dynamics to permit disconnected clusters.

Related Experiment Videos

  • High-precision transition location via comparison of the largest and second-largest clusters.
  • Finite-size scaling analysis to reveal properties not accessible through analytical solutions.

    • Main Results:

    • Identified critical features of the percolation transition that differ from dilution in fully grown networks.
    • Observed power-law behavior for the order parameter (p-p(c))^(-zeta) with zeta ≈ 4, deviating from stretched exponential behavior.
    • Found that the Berezinskii-Kosterlitz-Thouless scenario does not apply to this model.

    Conclusions:

    • The modified Barabási-Albert model provides new insights into percolation on growing networks.
    • The observed power-law behavior suggests unique critical phenomena distinct from other growing network percolation models.
    • The crossover number of nodes N(x) plays a key role in describing the giant cluster phase, characterized by power-law scaling.