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Degree-ordered percolation on a hierarchical scale-free network.

Hyun Keun Lee1, Pyoung-Seop Shim2, Jae Dong Noh3

  • 1Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea and School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea.

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We studied degree-ordered percolation (DOP) on flower networks. For u≠1, DOP matches bond percolation; for u=1, thresholds match but behaviors differ, impacting epidemic spreading models.

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Area of Science:

  • Statistical Physics
  • Network Science
  • Complex Systems

Background:

  • Percolation theory is crucial for understanding network connectivity.
  • Degree-ordered percolation (DOP) introduces a unique node-linking mechanism.
  • Hierarchical flower networks offer a complex topology for analysis.

Purpose of the Study:

  • Investigate critical phenomena of the DOP model on hierarchical (u,v) flower networks.
  • Analyze the impact of the parameter 'u' on percolation behavior.
  • Explore implications for epidemic spreading models.

Main Methods:

  • Employed a renormalization-group-like procedure.
  • Derived recursion relations for percolating probability and order parameter.
  • Calculated percolation thresholds and critical exponents.

Main Results:

  • For u ≠ 1, DOP critical behavior mirrors bond percolation with a shifted, non-zero threshold.
  • For u = 1, DOP and bond percolation share a vanishing threshold but exhibit distinct critical behaviors.
  • The findings reveal differences in network resilience based on the DOP model's parameter 'u'.

Conclusions:

  • The DOP model's critical phenomena on flower networks are highly dependent on the parameter 'u'.
  • Distinct behaviors for u=1 and u≠1 suggest different network robustness and information flow characteristics.
  • Understanding these phenomena is vital for modeling epidemic spreading and other network-dependent processes.