Shortest path tree-based algorithm for efficient resilience measures

This work introduces a novel resilience measure for complex networks, addressing both theoretical and empirical aspects within infrastructural and financial contexts. The core contribution is a modified version of a label-correcting algorithm (Resilient Shortest Path Tree algorithm), designed to assess the ability of nodes to absorb shocks propagating along minimum-weight paths, while overcoming the computational limitations of previous approaches. The proposed method enables resilience computation in polynomial time, even for large-scale networks, while retaining the principal informational features of more accurate measures. The procedure is empirically validated through two large datasets: the US commercial airports network and financial interbank networks from the Bank for International Settlements (BIS), with analysis covering hundreds of simulated scenarios. Results demonstrate that the new resilience measure faithfully reproduces key stability and robustness properties of the observed systems, allowing differences in shock absorption capacity to be identified as a function of network topology and characteristics. Applications confirm the computational efficiency of the algorithm, especially for empirical research on complex networks in economic and infrastructural settings.