A multi-factor integrated vulnerability assessment framework for multi-layer intercity road networks considering cross-layer path selection

The previous studies on road network vulnerability often fails to fully account for the functional heterogeneity of different road layers and the resulting cross-layer path selection. In addition, the dynamic coupling effects among multiple factors, such as traffic demand and economic interdependence, during the disturbance evolution process have received limited attention. These limitations weaken the ability to identify the vulnerability characteristics of multi-layer intercity road networks (MIRNs). To address these gaps, this study proposes a vulnerability assessment framework that integrates network topology, traffic demand, and economic interdependence. First, an MIRN model is developed to capture the functional differences among expressways, national highways, and provincial highways, providing a foundation for incorporating the impact of cross-layer path selection. Second, by dynamically tracking the evolution of node betweenness centrality, traffic flow, and economic centrality, a dynamic integrated node importance model is constructed to quantify changes in the functional states of each node during each attack iteration. Based on this, the traditional network efficiency is revised by assigning weights according to the normalized values of dynamic node importance, enabling accurate detection of overall performance degradation. A case study on the MIRN of the Guangdong–Hong Kong–Macao region shows that the proposed framework not only reveals the mechanisms by which independent and combined factors affect the evolution of network vulnerability, but also confirms the dominant role of network topology in shaping vulnerability. Moreover, the study finds that under specific attack scenarios, economic interdependence can be activated and intensified, thereby playing a positive role in sustaining network performance.