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Neighbor-induced damage percolation.

Lorenzo Cirigliano1, Claudio Castellano2

  • 1Università La Sapienza, Dipartimento di Fisica, Piazzale Aldo Moro, 2, I-00185 Rome, Italy.

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|June 19, 2025
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Summary
This summary is machine-generated.

Neighbor-induced damage percolation reveals that systems can form a giant usable component (GUC) at a finite threshold. A damaged phase with a giant damaged component (GDC) appears in networks with sufficient connectivity.

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Area of Science:

  • Statistical Physics
  • Network Science
  • Complex Systems

Background:

  • Neighbor-induced damage percolation models systems where element inactivation damages neighbors.
  • Understanding the formation and behavior of usable and damaged components is crucial for system resilience.

Purpose of the Study:

  • To present an exact solution for the size of the giant usable component (GUC) and giant damaged component (GDC) in uncorrelated random graphs.
  • To analyze the impact of network connectivity and heterogeneity on component formation and critical exponents.

Main Methods:

  • Exact solution for GUC and GDC in uncorrelated random graphs.
  • Analysis of critical exponents and phase transitions.
  • Numerical simulations on D=2 regular lattices.

Main Results:

  • The GUC appears at a finite threshold, exhibiting homogeneous mean-field percolation critical exponents.
  • Network robustness is maximized at an optimal average degree.
  • A damaged phase with a GDC emerges at high average degrees, bounded by two percolation transitions.
  • New critical exponents are observed for GDC dismantling in scale-free networks.

Conclusions:

  • The formation of the GUC is robust across different network connectivities.
  • The existence and behavior of the GDC depend on network properties like average degree, spatial dimension, and coordination number.
  • Scale-free networks exhibit unique critical behavior during GDC dismantling.