Study on the robust control of higher-order networks.

With the development of information technology, the interactions between nodes are no longer restricted to two nodes. Recently, researchers have proposed a higher-order network, which is more suitable to describe the multidimensional interaction relationships in systems. A higher-order network with good robustness can effectively resist natural disasters and deliberate attacks. How to improve the robustness of the higher-order network is worth studying. In this paper, we construct two higher-order networks based on the simplex structure. In addition, we propose a capacity load model that can describe the robustness of higher-order networks. The simulation results show that the robustness of the higher-order network is positively correlated with the size of the high-order network, the larger the size of the higher-order network, the more robust the higher-order network is in two attack strategies. In addition, the robustness of higher-order is related to the number of 2-simplexes in the network. Furthermore, the robustness is affected by the weight coefficients of 1-simplex and 2-simplex interactions. Therefore, we can improve robustness of higher-order networks by controlling the weight coefficients of the 1- and 2-simplex in higher-order networks. We verified the conclusions by two synthetic higher-order networks and a constructed higher-order network based on real data.