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The robustness of metro networks with the rich-core structure

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  • Liu, Zhihang
  • Li, Wei
  • Yang, Yuxiang

Abstract

As a critical component of daily transportation, it is crucial to investigate how metro systems maintain stable operations in the face of various internal and external anomalies and attacks. Researching the robustness of metro networks with the rich-core structure can effectively reveal the vulnerabilities of critical nodes, thereby providing important insights for optimizing network design and enhancing transportation efficiency. In this work, we demonstrate several characteristics of metro networks: the degree distribution follows a power-law; the node betweenness is more continuous than the degree values; and the relation between the rich-club coefficient and the sequence of nodes ranked by betweenness follows an inverse proportional function. Based on these characteristics, we propose an algorithm to identify rich-core structures in metro networks, which includes the high-betweenness nodes we require. Since the edge weights are primarily concentrated between high-betweenness nodes, our algorithm is also applicable to weighted metro networks. We then investigate the robustness of six well-structured metro networks by simulating random and targeted attacks on the rich-core. The results indicate that, in the majority of metro networks (both weighted and unweighted), it is crucial to enhance protection against random attacks on the rich-core, as random attacks on this core can have effects comparable to targeted attacks. However, for a few networks with high edge weights in the rich-core, such as the Berlin metro network, the impact of targeted attacks far exceeds that of random attacks. In such cases, special attention must be given to protecting high-betweenness nodes to prevent rapid network collapse.

Suggested Citation

  • Liu, Zhihang & Li, Wei & Yang, Yuxiang, 2025. "The robustness of metro networks with the rich-core structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 657(C).
    • Handle: RePEc:eee:phsmap:v:657:y:2025:i:c:s0378437124007398
    DOI: 10.1016/j.physa.2024.130230
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    References listed on IDEAS

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