Revealing higher-order interactions through multimodal irreversibility in flood-affected transportation networks

Climate change and extreme weather events increasingly threaten urban transportation systems, challenging their ability to maintain essential mobility services. Current analytical approaches primarily focus on individual modes or simplified interactions, failing to capture the complex, non-equilibrium dynamics that emerge when multiple transportation modes interact under stress. This research introduces a novel Multi-modal Visibility Graph Irreversibility (MmVGI) framework for analysing 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. While primary roads maintain stable dynamics dominated by motorised transport, secondary networks show complex patterns of modal interaction, with cycling emerging as a crucial component in system adaptation. The strong correlation between unique and combined irreversibility measurements provides evidence for genuine higher-order interactions that cannot be reduced to simpler modal combinations. These findings advance both theoretical understanding of urban system dynamics and practical approaches to transportation management, offering valuable insights for urban planners and policymakers in developing more resilient, adaptive transportation systems for future climate challenges.