Horizontal Visibility Graph Construction And Backbone Structure Identification Of Interdependent Networks

Today,in the 21 st century,the connections between the various environments have become closer and more complex in our lives.Interdependent networks explain these relationships from the perspective of complex networks using the topology information of the networks.It is a hot topic with important theoretical and practical significance for the research of the internal structure of subnets and the backbone structure between subnets of interdependent networks.In this paper,the construction and structure identification of interdependent networks are investigated.The main research contents and innovations are as follows.(1)Based on the time series and horizontal visibility graph,a new method for constructing interdependent networks is proposed.The core idea of this method is that pre-processing the original sequence,calculating the arithmetic mean of the node values with different scales,and then,we transform the original time series into a new sequence.Then,the horizontal visibility graph is used to construct an interdependent network model for the new sequence.Taking the periodic time series and white noise sequence as examples,an interdependent network is constructed with the proposed algorithm.We analyze its static feature.The results show that when the scale of the box increases,the average degree of nodes in the networks decreased initially,followed by an increase.The clustering coefficient increases firstly,then decreases and but again increases.The average path length of the network always increases.Therefore,we can control the size of the box to achieve the most needed and optimal network.(2)The problem of identifying the backbone structure of a directed interdependent network consisting of two subnets is discussed.Connections in this network exist only between subnets and have non-linear connections,and there is no connection in the two subnets.Based on Lyapunov stability theory,adaptive synchronization control technology and linear matrix inequality method(LMI),some sufficient conditions for the adaptive synchronization of the drive network and the response network are proposed.These conditions guarantee the identification of the backbone structure of the drive network while the two networks achieve their synchronization.The final numerical simulations verify the correctness and effectiveness of the theory presented in this paper.