A social cost gradient centrality for transportation networks

Abstract Urban road networks are prototypical complex systems in which large numbers of individual agents interact through shared infrastructure, giving rise to collective traffic equilibria. These equilibria emerge from decentralized route choice decisions and exhibit a strong sensitivity to local changes in network properties. Even small modifications to the capacity or free-flow travel time of a single link can trigger large-scale reconfigurations of traffic flows, as illustrated by the Braess paradox. Conventional measures of link importance often overlook this systemic sensitivity and its implications for network efficiency. In this study, we introduce a social cost-based centrality measure that quantifies the marginal impact of link-level free-flow travel time perturbations on total social cost under Wardrop equilibrium. The measure is derived analytically from the linear formulation of the traffic assignment problem, enabling efficient and interpretable computation of local sensitivities on fixed active-support subgraphs (and thus piecewise linear behavior across regime changes). We demonstrate the approach in synthetic and real-world urban networks, revealing structurally critical links that exert disproportionate influence on travel costs. Beyond improving network efficiency, this framework supports targeted interventions that can reduce unnecessary travel, lower emissions, and contribute to the transition toward more sustainable and livable cities.