The Impact of Higher-Order Motifs on Interdependent Power-Communication Networks

The interdependent power-communication network is one of the most important infrastructures in modern society. Modern power systems rely heavily on communication networks for real-time monitoring and control, and communication networks require stable power supplies. This complex interdependence brings significant risks, especially in the case of cascading failures, which may spread rapidly in interconnected systems. Since power grids are exposed to the wild for a long time, they are highly susceptible to natural disasters and trigger cascading failures. However current researches mainly focus on studying the robustness of complex systems from low-dimensional nodes or edges and ignore the interaction between local structures. Motifs are a higher-order structures, providing a new view for studying complex systems. In this paper, we study the impact of the robustness of interdependent power-communication networks based on motifs. Firstly, we construct a realistic model of interdependent power-communication networks by combining electrical properties and network delays. Then, we study the impact of motifs on the power grid. Through numerical simulations, we find that when about 20% of the power grid lines are removed, the motif concentration of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M_{42}$</tex> is close to 0, and the same is true when the communication network lines are removed, which indicates that motif <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M_{42}$</tex> is of great significance to maintaining the power grid topology. We think that this paper is helpful for designing more robust interdependent power-communication networks.