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Phase transition behavior of finite clusters under localized attack.

Ting Qing1, Gaogao Dong1, Fan Wang1

  • 1School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, China.

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Summary

Localized attacks (LA) impact finite clusters in complex networks. This study reveals a new scaling relationship and critical exponent, improving understanding of network vulnerability and infrastructure design.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Previous research on network robustness primarily focused on the giant component under attacks.
  • Localized attacks (LA) are crucial for understanding local failure diffusion in real-world networks.
  • The phase transition behavior of finite clusters under LA remains poorly understood.

Purpose of the Study:

  • To develop a theoretical and simulation framework for studying the phase transition of finite clusters under LA.
  • To analyze the impact of localized attacks on the structural robustness of finite clusters in complex networks.
  • To investigate the relationship between finite cluster size and network vulnerability.

Main Methods:

  • Development of a percolation framework for theoretical and simulation-based analysis.
  • Investigation of finite clusters with sizes greater than or equal to s (s=2, 3, ...).
  • Application of the framework to both random and real-world network models.

Main Results:

  • Random networks exhibit second-order phase transition behavior under LA.
  • The critical threshold (pc) increases with finite cluster size (s), indicating increased vulnerability.
  • A novel scaling relationship with critical exponent δ=-2 was discovered between the fraction of finite clusters and s.

Conclusions:

  • The study provides a theoretical framework to understand the phase transition of finite clusters under localized attacks.
  • Findings highlight the vulnerability of networks to LA, particularly concerning finite cluster behavior.
  • The developed framework and results can inform the design of more resilient critical infrastructures.