Enhancing robustness of higher-order networks with community structures through strategic edge addition

Higher-order networks are capable of capturing higher-order interactions among individuals that go beyond simple binary relationships. Networks with high robustness can effectively resist internal interference and external attacks. Therefore, developing strategies to improve the robustness of higher-order networks is very necessary and important. Meanwhile, the community structures of higher-order networks can have a significant impact on the robustness of these networks. However, the robustness enhancement mechanism of higher-order networks with community structures remains unexplored. In this paper, we propose network regulation strategies to enhance the robustness of higher-order networks with community structure through the strategic placement of higher-order structures at distinct topological positions. We also employ the load redistribution model for higher-order networks with community structures to simulate cascading failure processes. By observing the changes in the critical behavior of higher-order synthetic networks and real-world networks under different enhancement strategies, we find that for networks with clear community structures, adding higher-order structures among communities is more effective in enhancing network robustness, whereas for networks with ambiguous community structures, adding them within communities yields better outcomes. Additionally, a mixed higher-order structures addition strategy can be superior to a single-position addition strategy in certain networks. We also compare the results of the strategies of adding higher-order structures with the strategies of randomly adding edges and find that adding higher-order structures can more efficiently improve network robustness. This study contributes to a deeper understanding of the structure and cascading failure dynamics of high-order networks and lays the foundation for developing better robustness enhancement strategies.