The Research On Controllability,Degree Balance And Optimization Strategy Of Complex Networks

The controllability of complex networks is a hot issue in the field of network science in recent years.In 2011,a theoretical framework to study the structural controllability of an arbitrary complex directed network was presented,thus solving the problem that classical control theory is not suitable for large networks.This opened up a new way for studying control on complex networks.Subsequently,the effects of various network structure characteristics on network controllability were gradually revealed.However,many problems in the controllability of complex networks still need to be further studied.Starting from the degrees of single nodes,this thesis introduces a degree bal-ance index of the whole network on the basis of the difference between the out-degree and the in-degree of every node.By adjusting the degree balance of the network,its influence on the network controllability is observed.The results of numerical simulations show that under the condition of preserving the network size and average degree,the more balanced the out-and in-degrees of nodes are,the better the network controllability is;otherwise,the worse the network controllabil-ity is.In this thesis,the degree correlations of networks are also calculated with the variation of the degree balance,and it is found that there is a certain relation between the degree correlations and the degree balance.These results can play an active role in the construction and optimization of networks,and help to improve the control theory on complex networks.By adjusting the degree balance,the controllability of complex networks can be improved to a certain extent,but this method is less efficient and has a very limited range of adjustment.In order to more efficiently improve the controllability of complex networks and achieve the optimal results,from the maximum matching algorithm,this thesis transforms the matching paths and isolated nodes in networks into closed loops by adding links.The results of numerical simulations show that the optimization strategy of this thesis has better robustness,which can efficiently improve the controllability of complex networks and is easier to implement in some cases.Thus,it can provide a new idea for the design and optimization of real networks.