Quantifying higher-order modal interactions in urban transportation: a visibility graph approach to extreme weather adaptation

Climate change and extreme weather events increasingly challenge urban transportation systems' ability to maintain essential mobility services. While existing research has examined individual transportation modes or simplified interactions, the complex dynamics emerging from multi-modal interactions under stress remain poorly understood. This study introduces the Multi-modal Visibility Graph Irreversibility (MmVGI) framework to analyse transportation system behaviour during extreme weather events. By integrating concepts from non-equilibrium dynamics with visibility graph analysis, our approach quantifies complex interactions between different transportation modes and reveals the underlying mechanisms driving system non-equilibrium characteristics. Through a case study in the City of London during an extreme rainfall event, we demonstrate that transportation system adaptation exhibits clear hierarchical patterns across different road types, with cycling emerging as a crucial component in system adaptation. These findings offer valuable guidance for urban planners and transportation engineers in developing targeted resilience strategies during increasingly frequent extreme weather events.