Quantum percolation based dynamic propagation connectivity for critical-area identification in transport networks

Transport networks often lose functionality through gradual degradation in link operating conditions before topological disconnection occurs.

Link-centred and binary percolation measures identify important facilities or connectivity failures, but they provide limited information on which spatial areas cause the largest loss of network-wide propagation capability.

This paper develops a Dynamic Propagation Connectivity (DPC) metric based on quantum percolation for critical-area identification in transport networks.

Time-varying link travel times are converted into continuous propagation strengths, which define a Hermitian propagation operator at each observation time.

Candidate regions are then evaluated by a regional degradation experiment that measures the resulting loss of DPC.

The method is applied to a benchmark Sioux Falls network and six Florida road networks during the post-Hurricane Irma disruption and recovery period, using 1,281 five-minute observation times.

The benchmark confirms that the regional DPC score identifies a predefined structurally critical corridor.

In the Florida networks, the identified critical areas differ from regions selected by link count, local degradation, edge betweenness, algebraic connectivity, and classical percolation.

In Networks 1 to 4, DPC and classical percolation rankings have negative Spearman correlations, showing that continuous propagation degradation and binary fragmentation reveal different vulnerability patterns.

Robustness tests under alternative travel time scaling, degradation strength, and grid size show stable results, with mean rank agreement between 0.84 and 0.96.

The findings extend transport resilience analysis based on percolation from binary connectivity loss to continuous propagation degradation and provide a spatial diagnostic tool for regional monitoring, emergency planning, and recovery prioritisation.