Study on the Robustness of High-low-order Coupling Networks
This paper proposes a high-low-order coupled network model to gain a deeper under-standing of the interdependent relationships in real-world network systems and address the cas-cade failure issues faced by complex networks and their higher-order networks.This model de-scribes the interdependencies between complex networks(lower-order networks)and their high-er-order organizations(higher-order networks).Their vulnerability is analyzed by subjecting the high-low-order coupled networks to random attacks.The study reveals that high-low-order cou-pled networks exhibit greater vulnerability to random attacks than standalone lower-order net-works.This finding underscores the importance of considering the interdependencies between high and low-order networks in designing and managing complex network systems,particularly in preventing cascade failures,where special attention should be paid to the vulnerabilities of these interdependent structures.