Order Structure Analysis Of Node Importance Of Dynamic Multilayer Network

The complex networks are the simplification symbols and abstraction characteristic performances,which denote the interaction structure of a complex system from local to global interactions between individuals,and these sets and clusters of interactions and at same time belong to the systematic spatio-temporal multi-scale complexity.Temporal networks describe the changes and relationships in the interaction order of network nodes in the process of spatio-temporal evolutions.Multilayer networks are an extension of traditional networks in the spatial dimension,and dynamic multilayer networks can more effectively portray real-world complex systems.Therefore,the study of dynamic complex networks is important in terms of both theoretical significance and practical value.In this paper,we focus on the following key issues with modelling the temporal evolutionary system of super-neighbourhood association features and node importance(sequence structure)identification of dynamic complex networks(temporal networks,dynamic multilayer networks).First,in this paper,it describes the research background and significance in the context of the development history of complex networks in network science,and reviews domestic and international references on node importance identification methods for traditional complex networks and dynamic complex networks,and gives the relevant underlying theory.Second,to address the problem of node importance identification in temporal networks,an important node identification system method is proposed based on the dynamic evolution of inter-layer isomorphism rate of temporal networks with superneighbourhood matrix modelling.Relying on the inter-layer temporal association coupling relationship of complex networks,the coefficients of the integrated approximation relationship between adjacent and cross-layer networks are defined.Then,the super-neighbourhood matrix of the temporal network is constructed based on the intra-layer connectivity and inter-layer approximation relations.Again,the nodes in the temporal network are ranked in importance using the eigenvector centrality method,and the temporal global efficiency difference is calculated analytically and verified by the Kendall correlation coefficient.In the end,the empirical data simulations show that the Kendall’s τ values obtained from this paper’s model are on average improved by up to8.37% and 2.99% at each time layer when compared with the classical time-series network model,and the conclusion indicates that the metric of inter-layer isomorphism rate of the temporal network is scientifically valid.Final,for the analysis of the importance order structure of dynamic multilayer network nodes,a model of the importance order structure of nodes evolving in the time sequence of dynamic multilayer network super-neighbourhood association features is given.Relying on the inter-layer coupling geometric projection relationship of multilayer networks,the tensor algebra operation of association strength between nodes of dynamic multilayer networks at time t is defined,and then the dynamic multilayer network temporal inter-layer approximation coefficients at different times are proposed,and the super-neighborhood association feature matrix model is constructed.Again,a model for the evolution of the importance order structure of dynamic multilayer network nodes is constructed based on the centrality of dynamic complex network feature vectors,and the reliability of the model is verified by applying the SIR propagation model.Moreover,an improved ranking aggregation model for dynamic multilayer networks is proposed to further analyse the node importance order structure evolution law in full time.In conclusion,the empirical data simulations show that the Kendall’s τ values obtained from this paper’s model compare with the aggregated temporal network,and the overall improvement in each time layer is up to 15.2% and 13.29%,and the model conclusion indicates that the measure of the super-neighbourhood association feature of the dynamic multilayer network is scientifically valid.