The Research Of Complex Networks Resilience Based On Importance Measures

There are many complex systems closely related to our lives in real life,which requires us to conduct in-depth research on these complex systems in order to better reflect the characteristics of complex systems and solve problems in real life.However,with the acceleration of the process of globalization and the development of science and technology,the network of complex systems has become larger in scale and more complex in structure.The nodes in the complex system are also more closely connected,and these nodes are more vulnerable to damage and failure,which will have a significant impact on the complex system network.When a multi-node failure occurs in the network,the best solution is to recover the complex system network to the greatest extent in the shortest time from the perspective of recovery.The research on the resilience of complex networks has limitations due to the complex dynamics involved in system networks.Therefore,the research on the resilience of complex networks has practical and theoretical significance for solving the problem of multinode failure in actual complex networks and reducing economic losses.In this paper,the resilience and node importance measures models of complex networks are discussed from different perspectives.A mathematical model is established according to the research problem,and the model is solved.The main research content is divided into three parts:Firstly,in order to study the change of resilience in complex networks with multipoint failures,a residual resilience of complex networks is established from the perspective of loss,and the resilience model of complex networks is established from the perspective of recovery.Based on the residual resilience model and resilience model,the minimum residual resilience model and the maximum resilience model are established,and the residual resilience and resilience change of complex networks are studied from a dynamic point of view.Then,in order to study the optimal recovery sequence of failed nodes and edges in complex networks with multi-node failures,the minimum residual resilience model of complex networks and the classical importance model are combined to form the optimal repair time residual resilience importance measure,Birnbaum residual resilience importance measure,risk added worth residual resilience importance measure and risk reduction worth residual resilience importance measure.Using the Copeland method,a comprehensive analysis of the four residual resilience importance values was performed.The influence of the change of the recovery sequence of failure points on the reduction of residual resilience of complex networks under different importance degrees are studied.Finally,from the perspective of the vulnerability and recovery of complex networks,the loss importance measure model,recovery importance measure model and comprehensive importance measure model of complex networks are established to study the importance of failed nodes and edges in complex networks.Under the constraint of recovery cost,based on the maximum resilience model of complex networks,the influence of the recovery sequence of failed nodes and edges on the resilience recovery of complex network are studied.Based on the above research content,two model is established by taking the maritime network and transportation network as examples to study how to quickly and accurately evaluate the importance of the failed nodes and edges in the network when multiple nodes and edges fail in the network.In this way,it can quickly restore the failure point that has a greater impact on the rapid reduction of the remaining resilience of the network,or the rapid increase of the resilience,which can better control and predict the development of the entire network and reduce economic losses.