Robustness of interdependent directed hypergraphs with completely connected component

Directed hypergraphs (DH) provide a powerful framework for characterizing directional influences and higher-order interactions in complex systems. In many real-world systems, the group interactions represented by directed hyperedges generally have an inherent requirement of integrity, meaning their functionality depends on the simultaneous presence of all participating nodes. Traditional definition of strongly connected components that was proposed for classic directed graphs do not explicitly capture this requirement, which may lead to biased evaluation in the robustness of the system. To address this issue, we introduce the concept of the Completely Connected Component (CCC) of DH as a pertinent representation for such connectivity. By requiring that every directed hyperedge should satisfy the integrity condition, the CCC ensures the preservation of nodes incident to related hyperedges. In this paper we study the robustness of interdependent DH from the perspective of CCC, which has wide applications in many real-world systems. Based on a bipartite representation of DH, we develop a theoretical framework for analyzing the system. We systematically evaluate the system’s robustness under different types of interdependencies induced from CCC. Our analysis shows that the requirement of the integrity of hyperedges will markedly influence the robustness of the system, which is verified with numerical simulations. Specifically, since the CCC condition reinforces the preservation of nodes, interdependence between hypergraphs that takes place on nodes typically exhibit stronger robustness than that involving hyperedges. However, the system could be more vulnerable when the initial damage targets nodes rather than hyperedges. By analyzing the competing effects induced by the CCC on both the initial damage and the objects involved in the interdependence, non-monotonic behaviors of the system robustness are revealed. Our finding offers a deeper understanding of the robustness of systems with high-order interactions across various interdependence scenarios.