Assessing multilayer network robustness under asymmetric coupling using motif entropy

Asymmetric couplings are a defining feature of many real-world multilayer networks, arising from inherent structural properties rather than random configurations. These asymmetric relationships, which vary in both strength and direction, significantly influence network dynamics and robustness. This study presents a novel framework for quantifying these couplings and introduces motif entropy as a metric for assessing network robustness, based on higher-order topological interactions. Through extensive numerical analyses of a synthetic and three empirical multilayer networks, we explore the impact of asymmetric coupling and targeted attacks on different layers of the system on its robustness. Our results reveal that asymmetric coupling increases the complexity of cascading failures, with the dynamics of failure propagation being strongly dependent on the specific layer targeted by the attack. Notably, networks with a higher proportion of weak couplings exhibit enhanced robustness, as these interlayer dependencies disperse the impact of cascading failures, mitigating the risk of widespread disruption. These findings underscore the pivotal role of asymmetric coupling in determining network robustness, with weak couplings acting as a buffering mechanism that dampens the severity of cascading failures, while strong couplings heighten vulnerability under targeted disruptions.