Growth Challenges of Scale-Free Networks With Small Power Exponents

Chunlei Liu, Kai Hu, Jinshu Han and Li Qin

Discrete Dynamics in Nature and Society, 2025, vol. 2025, 1-12

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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:9435165

DOI: 10.1155/ddns/9435165

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