An explanatory composite metric for air cargo network robustness: incorporating pairwise synergistic effects

Understanding and enhancing network robustness is crucial for the stability of critical infrastructure systems such as air cargo transportation. Traditional studies on network robustness often focus on simulating random or targeted failures by progressively removing nodes or edges and analyzing the degradation curves. However, these approaches often overlook the pairwise synergistic effect: the extent to which two nodes jointly contribute to network robustness in a nonlinear manner beyond their individual impacts. Moreover, the current network robustness metrics, such as global efficiency and natural connectivity, can only measure the robustness from certain aspects, which can barely provide comprehensive insights. Therefore, the aims of this study include quantifying such pairwise synergy of air cargo network robustness. Besides that, a composite metric of network robustness is proposed by integrating multiple robustness metrics, including changes in global efficiency, natural connectivity, and local efficiency, using an entropy-weighted normalization method. This composite metric is utilized to calculate pairwise synergistic effect scores for node pairs. Moreover, this study employs the Multiple Regression Quadratic Assignment Procedure, to study the relationships between node pairs' features and the pairwise synergistic effect. This work contributes an approach for identifying critical node pairs whose simultaneous failure would disproportionately impair network performance.