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Shortest-path percolation on scale-free networks
Minsuk Kim1, Lorenzo Cirigliano2, Claudio Castellano3
1Indiana University, Bloomington, Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Indiana 47408, USA.
Physical Review. E
|February 20, 2026
Summary
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.
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.
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