Robustness And Control Of Complex Networks With Community And Dependency Relationship Underlying Random Risk

Whether in academia or industry,the integration of computer science and other majors is in the ascendant,which is not only the cross application of tools and models,but also greatly promotes the combination of thinking.The main content of this paper is to establish a statistical physical model in theory to simulate a practical network close to reality,so as to reflect the influence of the cascade process on the whole complex system through the network robustness index,and finally put forward a simple and effective algorithm to remedy the system collapse caused by the initial failure of the network.The physical model used in this paper is called complex network,which is mainly based on the topological structure of nodes and connecting edges to reflect the physical or logical connection between system elements,so as to use certain measurement indicators to study the relevant laws of the system.In order to simulate the real world,researchers have established a large number of network models.For example,in order to study the influence of spatial location,scholars have established a spatial embedded network model.Moreover,in order to study the interaction of systems composed of multiple isolated networks,researchers have established a interdependent network model and a multi-layer network model.In this paper,it is noted that many networks in the real world have the structure of community,and there is a strong interaction between the isolated networks of the same complex system,so the community dependent network model is introduced innovatively.For the interdependent modular network,two of the most important attributes are community and dependency.Their organic combination plays an important role in describing many system laws in the real world.For example,the power grid in the same city is obviously more dense than the transmission lines across cities,and the local close connection of this network is called community.Similarly,the communication network which controls the transmission network has such community characteristics.The two networks are not completely isolated,because the transmission network needs to provide energy for the communication network,which in turn can control the power grid.If a base station of the communication network loses its function,the power station controlled by the communication base station will lose its function immediately.Otherwise,if a power station in the transmission network loses its function,the communication base station responsible for providing energy by the power station will lose its function immediately.This phenomenon of interdependence between the two subnets is the dependency between the real networks.Obviously,many real systems are not only dependent or modular.The system composed of transmission network and power control network has both of these characteristics.However,this kind of interdependent modular network is not a simple addition of community network and interdependent network.This paper finds that this network model which takes into account the characteristics of both dependence and community has many unique and complex properties,so it is necessary to study the interdependent modular network model specifically.The main research work of this paper includes three aspects:the mathematical model of community dependent network,network robustness and recovery strategy.First of all,using the theory of random graph and the previous research on ER community network,this paper deduces the mathematical model of SF community network in detail,and constructs a complete interdependent modular network model by coupling the two parameters of couple density and noise coefficient.On the basis of the mathematical model,this paper also analyzes the influence of the number of communities,the probability of internal and external connecting edges and other parameters on the number of bridge nodes,the number of bridge edges and the modularity.Then,by studying the robustness of interdependent modular networks under random attack,it is found that the increase of the number of communities will make the P? curve show an obvious "thick tail" phenomenon,while the larger ?is,the lower the risk of complete collapse of the interdependent modular network is.Finally,as the core content of this paper,in order to effectively control the cascading process of interdependent modular networks,this paper proposes MSS algorithm to dynamically recover the interdependent modular network,taking into account the community and dependency.Through a large number of computer simulation experiments,it is proved that MSS algorithm not only has the best recovery effect under any attack strategy,network topology(ER and SF),number of communities,probability of internal and external connecting edges,noise coefficient and other parameters.However,for low coupling density and high recovery ratio,the difference between MSS algorithm and other recovery algorithms is very small.The main innovations of this paper are as follows:Firstly,in this paper,we use ER community network to build SF community network which accords with power law distribution,so that the interdependent modular network can simulate more real situations.Secondly,different from the attack strategy for bridge nodes,this paper mainly studies the change rule of the interdependent modular network after suffering random failure.Thirdly,according to the characteristics of the interdependent modular network model,we propose an algorithm to deal with the initial failure.From the research of the text,it can be seen that the algorithm can improve the giant connected cluster and probability of the existence of GCC,and reduce the number of iteration of the cascade process under the same recovery ratio,which shows that the innovative algorithm proposed in this paper has the advantage of high recovery efficiency for the interdependent modular network.This paper not only deduces the mathematical model of ER and SF structure community network,but also discusses the robustness of the interdependent modular network under different parameters through a large number of computer simulation experiments.At the same time,in view of the two important attributes of community and dependency,this paper proposes the MSS recovery algorithm based on the summary of previous studies,and demonstrates the effectiveness of the algorithm through simulation experiments.Through the work of this paper,we hope to provide some reference value for the research of related models and the control of real world network.