Enhancing the resilience of the belt and road sea-rail multimodal transport network: A critical node identification method integrating cycle structure and persistent homology

Youpeng Lu; Xiaowei Chen; Fan Chen

doi:10.61089/x9pzyp23

Authors

Youpeng Lu School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, China Author https://orcid.org/0000-0002-8310-1194
Xiaowei Chen School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, China Author https://orcid.org/0009-0005-7986-3152
Fan Chen Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou, China Author https://orcid.org/0009-0002-4187-0494

DOI:

https://doi.org/10.61089/x9pzyp23

Keywords:

Sea-Rail Intermodal Transportation, Complex Networks, Network Resilience, Key Node Identification, Cycle Persistent Homology

Abstract

Key node identification in multimodal transportation networks is essential for improving operational efficiency, mitigating risk propagation, and enhancing network resilience. However, traditional centrality metrics often fail to capture higher-order topological support roles and structural-functional differences in coupled multimodal networks. To address this limitation, this paper proposes a node importance metric, CPHD (Cycle Persistent Homology–Degree), which integrates cycle-structure persistent homology with node degree information. The method constructs a multi-scale filtration process based on cycle structures within the second-order neighborhood of nodes, extracts persistent features of higher-order topological structures, and combines them with local topological attributes to evaluate node importance. Comparative experiments on four real-world networks indicate that CPHD achieves the best overall performance among the compared metrics, including Degree Centrality (DC), Betweenness Centrality (BC), Closeness Centrality (CC), K-core, and Cycle-Ratio (CR), in terms of propagation consistency, structural disruption capability, and ranking differentiation. Furthermore, a case study on the Belt and Road sea–rail multimodal transportation network demonstrates the effectiveness and interpretability of CPHD in complex coupled systems. The results indicate that CPHD provides a reliable and interpretable framework for identifying structurally critical nodes in multimodal transportation networks, offering a topology-based quantitative reference for resilience enhancement and critical infrastructure protection.

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