Research On The Effect Of Degree Correlation On The Controllability Of Complex Networks

Under the background of big data,information technology is developing rapidly,more and more data can be provided for research.This has also promoted the rapid development of various disciplines and has made many notable research achievements.Under the huge data background,computing power has been limited to a certain extent,and the fuzziness of the analytical model results in the difficulty of modeling large-scale complex models.Complex network is an efficient way to build models for complex systems,which helps us further understand the interaction between transmission power and internal structure of complex systems.Therefore,the related research of complex network has become a hot research field,especially how to control a specific complex system effectively and efficiently.It has become the key theoretical basis of complex network area.For the actual complex systems such as smart grid,networking,real-time traffic system,disease transmission network,based on the complex network model on the research above the actual complex system,because of the different system has many common topology and dynamics,can contribute to the complex system itself has a more profound understanding,more comprehensive and more the objective of the.However,these types of complex systems are often degree dependent,so this paper will study the impact of degree correlation on network controllability.For a linear fixed length system,the purpose of controlling the whole system can be achieved by applying independent control signals to some nodes.These nodes that are applied to control signals are called drive nodes.The less the driver nodes in a network,the easier the network is to be controlled,the better the corresponding controllability.On the contrary,the more driving nodes in the network,the more control signals are applied to those driving nodes.The cost of control is very large,so the controllability of this type of network is very poor.Therefore,the proportion of the driving nodes in the network is a very important measure of the network controllability.However,for a specified network,the number of minimal nodes that needs to be controlled is certain.Not all of the nodes in the network need to be controlled,some nodes are always needs to be controlled,this kind of nodes is a key node;some nodes always need not be called redundant node control.Because redundant nodes are nodes that do not need to be controlled,the more the number of redundant nodes in the network,the less the number of drivers will be,and the controllability of the network will be better.The less the number of redundant nodes in the network,the less the nodes that do not need to be controlled,the worse the network controllability.At present,there have been the researchers discovered the redundant nodes in the network will appear the phenomenon of bifurcation is two different control models after the network average degree reaches a certain threshold: most of the nodes are redundant nodes in the network,nodes that need to be controlled is little: centralized control mode;only a few redundant nodes in the network.You need to account for the proportion of the control node will very decentralized control mode.This means that,when the average degree of the network in the network reached a certain threshold with the same statistical features of the network has two completely different physicalcharacteristics,the same statistical significance lies in the network has the same degree distribution and average degree,the physical meaning is quite different in different control modes.This paper extends the research of redundant nodes in complex networks,and joins the correlation of network degrees.By changing the degree of network correlation and the degree distribution of degree and degree of penetration,we can observe the change of redundant nodes in the network by changing the average degree of fixed network.According to the experimental phenomena,we observed the phenomenon of bifurcation of redundant nodes with the increase of the correlation degree of the network.This means that when the network has relatively high correlation,it can also cause the difference of network control models.The research of this paper is of great significance to the application of real network,because the real network often has some degree of correlation,rather than a simple random linked network.At present the network of relevant theoretical research still needs to improve the present situation,this paper puts forward a theoretical framework to study the correlation of the network controllability of evolution,is related to the characteristics of real network,in-depth study of the relevant network controllable effect can deepen to the surrounding complex system understand.The main work of this article is as follows:1,analyze the controllability of the network when the complex network is zero degree.In this paper,by finding the way of maximum matching in the network,the control nodes need to be controlled in the network.Because the nodes that need to be controlled are not static,we classify the nodes with whether the nodes in the root network participate in the network control and participate in the degree of network control.This paper analyzes the changing trend of different types of nodes in the network when the network is changing.In the zero dependent network,the controllability of the network will also change with the increasing of the average degree of the network.2,the influence of the different degree correlation on the network controllability is given when the complex network is dependent on the non zero degree.In order to make the theoretical research closer to the real network,the degree correlation coefficient of the network changes in a certain interval through the bilateral exchange process.In view of the directional property of the connection in the real network,a directed network is established.In the directed network,the moderate correlation coefficient is a correlation between the two nodes that are connected by a randomly directed connection.Therefore,the degree correlation is refined into four types,and the influence of the correlation of each degree on the number of redundant nodes is studied by simulation.Because the proportion of the redundant nodes in the network is different from the different control modes,the evolution of the two control models in the controllability of the network structure is mapped.3,Analyze the influence of four degree correlation on the complex controllability,and compare the conditions of the emergence of a special structure in the network.On the basis of the above,we also propose a mathematical framework to explain the influence of degree correlation on redundant nodes.In this paper,the effects of network averages and the degree distribution of network access degree on the control of network structure are considered.Finally,the effects of the degree correlation on the network controllability are summed up in combination with the experimental and theoretical analysis.4,analysis of network related effects of complex network controllability reasons,bycalculating the number of redundant nodes in the network to establish a formula for solving nodes become redundant nodes probability equation,equation effective solution and the number of redundant nodes are mapped to network state,which corresponds to the network controllability.Finally,the relevant work of this paper is summarized,and the future prospect of the research on the complexity of complex network controllability and degree is also made.Through the related research and analysis of this paper,when the characteristics of the average degree and degree distribution of the complex network are known,the degree correlation determines the network controllability to a great extent.And the influence of different types of degree correlation on network controllability is different,and the degree correlation of the same type is also different in the controllability corresponding to the correlation coefficient of different degree.Through verification and analysis of experiments,the degree correlation between random network and scale-free network will affect the controllability of complex networks in varying degrees.