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<p>As a critical foundation of air transportation, the airway network (AIN) plays an essential role in ensuring smooth flight operations. Analyzing and optimizing the structural characteristics of the AIN can help reduce flight delays and enhance the safety and reliability of air transport. In this paper, an order degree relative entropy (ODRE) model for the AIN is established based on information entropy theory. Simplified AIN models are constructed based on the actual Chinese AIN and its subnets in Beijing, Shanghai, and Guangzhou. Various attack strategies—random, degree, betweenness, closeness, eigenvector, and Bonacich centrality—are applied to the AINs. The ODRE is used to evaluate the comprehensive robustness of the AINs under these diverse attacks. Compared with traditional methods, the proposed ODRE in this paper significantly enhances the reliability and applicability of the system while maintaining consistency and stability in network efficiency. It enables a more precise assessment of AIN vulnerability under different attack scenarios and provides deeper insights into network structure and dynamics.</p>

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RETRACTED ARTICLE: Information entropy and relative entropy models for analyzing structural robustness in airway networks

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年11月11日

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  • Keyan Zhao,
  • Yanhua Li,
  • Guangjian Ren,
  • Zongqian Zhang

摘要

As a critical foundation of air transportation, the airway network (AIN) plays an essential role in ensuring smooth flight operations. Analyzing and optimizing the structural characteristics of the AIN can help reduce flight delays and enhance the safety and reliability of air transport. In this paper, an order degree relative entropy (ODRE) model for the AIN is established based on information entropy theory. Simplified AIN models are constructed based on the actual Chinese AIN and its subnets in Beijing, Shanghai, and Guangzhou. Various attack strategies—random, degree, betweenness, closeness, eigenvector, and Bonacich centrality—are applied to the AINs. The ODRE is used to evaluate the comprehensive robustness of the AINs under these diverse attacks. Compared with traditional methods, the proposed ODRE in this paper significantly enhances the reliability and applicability of the system while maintaining consistency and stability in network efficiency. It enables a more precise assessment of AIN vulnerability under different attack scenarios and provides deeper insights into network structure and dynamics.