Research On Robustness Of Edge-Coupled Independent Networks

There are various networks in the real world,such as transportation networks,power grids,and communication networks,which are closely related to our lives.However,these networks often do not exist in isolation.For example,the communication network needs the power support of the power grid,and the operation of the power grid requires the scheduling of the communication network and the energy supply of the transportation network.Therefore,there are interdependent relationships between the communication network,the power grid and the transportation network.Such complex systems consisting of multiple single networks are called interdependent networks.Due to the interdependence between networks,the interdependent network is more vulnerable than a single network,and it is easy to cause catastrophic consequences due to cascading failure.Therefore,the robustness analysis and optimization of interdependent networks has attracted more and more attention.Traditional research mainly focuses on node-to-node dependencies,but there are also edge-to-edge coupled interdependent networks in the real world.At present,such interdependent networks have not been addressed well.Therefore,this paper robustness of edge-coupling interdependent networks is studied.The main contributions of this paper are as follows:(1)Firstly,a comprehensive summary of the research status of interdependent network’s theory at home and abroad is discussed,and a detailed summary of the basic concepts and research methods of interdependent network’s theory is described,which provides a theoretical basis for the follow-up research work.(2)Considering that there are many networks in the real world,where there are some edge-to-edge coupling dependencies between networks with different topological structures and scales,a more generalized edge-coupling interdependent network model with arbitrary coupling strength is proposed,usingq_A andq_B represent the edge coupling strength of the network A and B,respectively.The theoretical analysis framework of this partial of the edge-coupling network is developed,and the phase transition behaviors of the system are analyzed and the phase transition thresholds of the system are calculated.In particular,the theoretical solution of partial of the ER-ER(Erd?s-Rényi network)edge-coupling network is carried out verified by numerical simulations.Further comparative research was conducted with the node-coupling network with the same coupling strength,and it is found that the robustness of the partially edge-coupling interdependent network is stronger than that of the partially node-coupling interdependent network under the same coupling strength,and it changes from the first-order phase transition to the second-order phase transition.The coupling strength critical point of the first-order phase transition is smaller than that of the partial node-coupling interdependent network.In addition,when the coupling strength is within a certain range,the network A will undergo a hybrid phase transition,and the range of the coupling strengthq_A does not change with the change of the average degree?k?value of the network when the hybrid phase transition occurs.(3)Aiming at the characteristic that the edges of one layer of network have multiple dependencies on the edges of another layer of network in the real-world interdependent network,a conditional dependent group percolation model based on edge-coupled interdependent network is proposed.The feature of this model is that one edgee_A of the network A depends on m(m?0)edges in the network B,and one edge of the network B depends on exactly one edge in the network A.The m edges is defined as the dependency group,and if the failure ratio of the edges in the dependency group don’t exceed the failure tolerance?(??[0,1)),this edge will survive,otherwise the edge will fail.In this paper,the theoretical analysis framework of the model is developed through generating function theory,and the giant components and phase transition thresholds of the network are calculated accordingly.In particular,simulations are carried out on ER-ER and RR-RR(Random Regular network)edge-dependent networks,which verifies the correctness of the theoretical analysis.The results show that for the same dependent group size,the robustness of the network is improved with the increase of?.AS the dependent group size changes,the phase transition behavior of the network changes from first-order to hybrid.