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Size-independent scaling analysis for explosive percolation.

Kenta Hagiwara1, Yukiyasu Ozeki1

  • 1Department of Engineering Science, Graduate School of Informatics and Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan.

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We developed a new scaling analysis for explosive percolation on random networks, improving critical exponent estimations. This method offers a reliable way to study phase transitions in network models like ER and dCDGM(2).

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • The Achliottas process exhibits explosive percolation, a rapid second-order phase transition in random networks.
  • Understanding the transition point and critical exponent β is crucial for network percolation theory.

Purpose of the Study:

  • Propose a novel system-size-independent scaling analysis to determine the transition point and critical exponent β.
  • Estimate β for product-rule (PR), da Costa-Dorogovtsev-Goltsev-Mendes (dCDGM, m=2), and Erdős-Rényi (ER) models.
  • Develop an extrapolation scheme using maximum cluster size for improved β estimation.

Main Methods:

  • Developed a system-size-independent scaling analysis for percolation on random networks.
  • Applied the analysis to PR, dCDGM (m=2), and ER models.
  • Introduced a maximum cluster size parameter for an extrapolation scheme to refine β estimations.

Main Results:

  • Validated the scaling analysis, particularly for determining the transition point.
  • Obtained β estimations consistent with previous studies for ER and dCDGM(2) models.
  • The extrapolation scheme improved β accuracy for ER and dCDGM(2), but PR model estimations showed larger deviations.

Conclusions:

  • The proposed scaling analysis is effective for studying explosive percolation and critical phenomena in random networks.
  • The extrapolation scheme enhances the accuracy of critical exponent β estimations.
  • Further investigation is needed for the PR model to reconcile deviations in β estimations.