Enhanced complex network analysis of multi-layer intercity road networks through identification of network-specific dynamics

The multi-layer intercity road network (MIRN), comprising expressways, national highways and provincial highways, displays complex topology and nonlinear responses to perturbations that differ significantly from those of general complex networks. Existing models often simplify MIRNs into single-layer or weakly coupled representations, thereby overlooking network-specific dynamics arising from structural heterogeneity and cross-layer interactions in path selection. To address this gap, an enhanced complex network analysis framework is developed that identifies cross-layer path selection behavior as the key mechanism driving MIRN dynamics. Toll effects on path selection are captured by an enhanced impedance function integrating road attributes, toll costs and congestion effects, which enables unified representation of road hierarchy, spatial demand and user decision-making. Using shortest travel time computed from this impedance, classical network indicators such as network efficiency, betweenness centrality and closeness centrality are redefined to reflect behavior-driven dynamics. Moreover, fine-grained indicators at the path and segment levels are introduced to reflect path preferences and flow reassignment under different toll strategies. These developments establish a causal chain linking toll strategies, cross-layer path selection behavior, and network-specific dynamics, revealing how economic incentives reshape network structure and function. Empirical simulations on the Guangdong–Hong Kong–Macao MIRN demonstrate that expressway tolling shifts large volumes to lower-grade highways, reduces network efficiency, and reconfigures node centrality. Even after toll removal, local bottlenecks and structural changes hinder full recovery, highlighting the irreversibility and path-dependence of MIRN dynamics.