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Growth Challenges of Scale‐Free Networks With Small Power Exponents

Author

Listed:
  • Chunlei Liu
  • Kai Hu
  • Jinshu Han
  • Li Qin

Abstract

Scale‐free networks with adjustable degree exponents (γ) are crucial for modeling various real‐world systems. In addition, generating them within the (2, 3] interval remains significant. This study proposes an improved preferential attachment model for γ adjustment. Network topological properties, including the mean shortest path length and clustering coefficient, are analyzed through simulations. Vulnerability to targeted attacks is also assessed. Smaller γ values lead to networks with shorter mean shortest path lengths and higher clustering coefficients but increased vulnerability to targeted attacks. When γ drops below 2.20, node pairing difficulties during edge formation rise sharply, causing edge establishment failures and impeding network growth. The model successfully generates scale‐free networks with tunable γ in the (2, 3] interval, revealing a trade‐off between network clustering, connectivity, and robustness. The findings offer insights into the design and analysis of real‐world scale‐free systems, emphasizing γ′s role in shaping network topology and resilience.

Suggested Citation

  • Chunlei Liu & Kai Hu & Jinshu Han & Li Qin, 2025. "Growth Challenges of Scale‐Free Networks With Small Power Exponents," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnddns:v:2025:y:2025:i:1:n:9435165
    DOI: 10.1155/ddns/9435165
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