Robustness of One-to-Many Interdependent Higher-Order Networks Against Cascading Failures

In the real world, the stable operation of a network is usually inseparable from the mutual support of other networks. In such an interdependent network, a node in one layer may depend on multiple nodes in another layer, forming a complex one-to-many dependence relationship. Meanwhile, there may also be higher-order interactions between multiple nodes within a layer, which increase the connectivity within the layer. Interlayer dependencies and intralayer connectivity may become key factors affecting network reliability, because failures within a layer will propagate to another layer through dependencies, and the cascading effects within and between layers may trigger catastrophic network collapse. However, existing research on one-to-many interdependence often neglects intralayer higher-order structures and lacks a unified theoretical framework for interlayer dependencies. Moreover, current research on interdependent higher-order networks typically assumes idealized one-to-one interlayer dependencies, which does not reflect the complexity of real-world systems. These limitations hinder a comprehensive understanding of how such networks withstand failures. Therefore, this article investigates the robustness of one-to-many interdependent higher-order networks under random attacks. Depending on whether node survival requires at least one dependence edge or multiple dependence edges, we propose four interlayer interdependence conditions and analyze the network’s robustness after cascading failures induced by random attacks. Using percolation theory, we establish a unified theoretical framework that reveals how higher-order interaction structures within intralayers and interlayer coupling parameters affect network reliability and system resilience. In addition, we extend our study to partially interdependent hypergraphs. We validate our theoretical analysis on both synthetic and real-data-based interdependent hypergraphs, offering insights into the optimization of network design for enhanced reliability.