Research On Robustness Of Network Of Networks Under Intentional Attack With Limited Information

With the rapid development of information technology,the coupling relationship between the actual systems is getting closer and closer.The network of networks(NON)formed by the interdependent coupling of multiple networks can effectively describe the coupling relationship between systems.Due to the characteristics of large-scale attributes and dynamic evolution,it is often difficult to obtain the edge connection information of all nodes in the network.Intentional failure under limited information can effectively make up for this deficiency,that is,select the node with the maximum degree value among random n nodes to analyze the robustness of the network.Based on this,in this thesis,we start from two interdependent networks,and further expands it to more generalized network of networks with different configurations,such as:star-like,tree-like,loop-like.The robustness of network of networks with different configurations under intentional attack with limited information is studied through analysis and simulation,respectively.In this paper,we propose a theoretical framework model of multiple interdependent networks under intentional attack with limited information.Using this framework,the robustness of two interdependent networks under intentional attack with limited information is studied.Through the numerical simulation of Erdos-Renyi(ER)network,Scale-Free(SF)network,Barabasi-Albert(BA)network and generating function theory,we analyze different parameters(coupling strength q,information index n,average degree(k)and power-law exponent A of network,etc.)on the robustness of the system.By adjusting the coupling strength q,it can be found that with the increase of q in the two partially interdependent networks,the phase transition behavior of the network gradually changes from a second-order continuous phase transition to a first-order hopping phenomenon.At the same time,with the growth of n,the critical threshold pc of the network gradually increases,that is,under the same conditions,when the information index n gradually changes from 1(ie random attack)to ∞(classical intentional attack),the robustness of the network is gradually weakened.But when n increases to a certain extent,the threshold point pc tends to be stable.For example,for ER interdependent networks,after n>10,pc does not change any more.In addition,the topological characteristics of the network itself also show a similar effect on the system robustness.For example,for SF interdependent networks,when the power-law exponent λ is small,λ and pc show a positive correlation,but with the increase of λ,pc also gradually remained stable and stopped growing.Further analysis shows that there is an obvious scaling relationship between 1/pc and 1/n,and the scaling exponent decreases with the increase of the coupling strength q.For network of networks of different configurations,the influence of several influencing parameters such as coupling strength q,information index n,average degree(k)and power-law exponent A of network on the robustness of the network of networks itself is similar to the results of the two interdependent networks.The number m of sub-networks in the system has no effect on the coupling strength q,the coupling strength q and the phase transition behavior,the correlation between the critical threshold pc and the information index n,and the stable value of the information index n when pc reaches stability,but it has no effect on the critical threshold.The effect of pc varies with the system configuration.For the network of networks under the star-like and the tree-like structure,pc increases with the increase of the number of sub-networks,but it shows the opposite correlation under the looplike structure.In this paper,we investigate the robustness of network of networks under intentional attacks with limited information,which helps to facilitate the design of infrastructure and provides new insights into the study of robustness and phase transition behavior of complex networks.