Method for Measuring Resilience of Complex Systems Using Network Theory and Graph Energy

Because of societies’ dependence on systems that have increasing interconnectedness, governments and industries have an increasing interest in managing the resilience of these systems and the risks associated with their disruption or failure. The identification and localization of tipping points in complex systems is essential in predicting system collapse but exceedingly difficult to estimate. At critical tipping-point thresholds, systems may transition from stable to unstable and potentially collapse. One of the approaches to measuring a complex system's resilience to collapse has been to model the system as a network, reduce the network behavior to a simpler model, and measure the resulting model's stability. In particular, Gao et al. introduced a method in 2016 that includes a resilience index that measures precariousness, the distance to tipping points. However, those mathematical reductions can cause the model to lose information on the topological complexity of the system. Using computational experimentation, a new method has been formulated that more-accurately predicts the resilience and location of tipping points in networked systems by integrating Gao et al.’s method with a measurement of a system's topological complexity using graph energy, which arose from molecular orbital theory. Herein, this method for measuring and managing system resilience is outlined with case studies involving ecosystem collapse, supply-chain sustainability, and disruptive technology. The precariousness of these example systems is found using the dimension reduction, and a graph-energy correction is quantified to fine-tune the measurement. Lastly, the integration of this method into systems engineering processes is explored to provide a measurement of precariousness and give insight into how a complex system's topology affects the location of its tipping points.