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Shortest-path percolation on scale-free networks.

Minsuk Kim1, Lorenzo Cirigliano2, Claudio Castellano3

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Physical Review. E
|February 20, 2026
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Summary
This summary is machine-generated.

The shortest-path-percolation model on scale-free networks shows a transition independent of the degree exponent, similar to Erdős-Rényi networks. This occurs because the process homogenizes network structure before the transition.

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Area of Science:

  • Network science
  • Statistical physics
  • Complex systems

Background:

  • The shortest-path-percolation (SPP) model simulates resource consumption and network breakdown.
  • SPP on Erdős-Rényi networks (ERNs) shows universality with ordinary bond percolation for finite budgets, but becomes more abrupt for infinite budgets.

Purpose of the Study:

  • Investigate the SPP transition on random scale-free networks (SFNs).
  • Determine if SFNs exhibit different percolation behavior compared to ERNs.

Main Methods:

  • Large-scale numerical simulations.
  • Finite-size scaling analysis.
  • Studied SPP on random scale-free networks with power-law degree distributions.

Main Results:

  • The SPP transition on SFNs is identical to that on ERNs, irrespective of the degree exponent.
  • The study distinguishes between finite- and infinite-budget SPP universality classes.
  • The SPP process homogenizes the heterogeneous structure of SFNs prior to the transition.

Conclusions:

  • The heterogeneity of SFNs does not influence the SPP transition universality class.
  • The SPP model provides a unified understanding of network transitions across different network topologies.