Measuring node importance in air transportation systems: On the quality of complex network estimations

Throughout the last two decades, many studies have used complex network analysis techniques to estimate the importance of airports for airline operations. Various node importance measures were exploited to obtain a ranking of airports for a given airline, to quantify the overall criticality for the airline at hand. However, neither of these measures have been evaluated against a realistic reference baseline. In this study, we propose a mixed-integer program formulation for an airline recovery baseline under node disruptions. Given the intrinsic complexity, we devise a variable neighborhood search heuristic to compute near-optimal solutions for real-size airline networks. We use the optimization-based recovery model to compare against the existing node importance methods in the literature, for a set of real airline operational schedules. Our experiments show that the existing simplifications based on complex networks often underestimate the effect of node failures and that there exist significant ranking mismatches especially for top-ranked nodes. We believe that our work helps to better assess the role of airports in airline networks, not only on the way towards providing a scalable operation-focused solution to the problem, but also by giving an empirical estimation regarding the quality of complex network abstractions used prevalently in the literature.