Research On Structural Characteristics Measurement Of Multilayer Networks

In the case of real-world networks,there are often interacting relationships between networks and networks,yet the study of single-layer networks can no longer accurately portray such complex network relationships.As a new research direction of complex networks,multilayer networks exhibit more complex topologies than single-layer networks.It is always an open topic to measure the characteristics of network structure.In this paper,two new measurement methods of node centrality and interlayer correlation of multilayer network are presented respectively from the local and the global levels,and empirical analysis is carried out.The main research contents and innovations of this paper are as follows:(1)Considering the local characteristics of multilayer networks,a new model for measuring node centrality in multilayer networks is constructed.Because the structure of multilayer networks is more diverse and there are more complex interlayer influences,the traditional measurement method of node centrality in single-layer networks is no longer suitable for multilayer networks.However,most of the existing multilayer network node centrality methods ignore the influence of the relationship between the network layers on the importance of nodes,or there are problems of high computational complexity and low efficiency.Therefore,the problem of information missing between layers of multilayer network is easy to occur in the calculation process,which leads to inaccurate evaluation results or the difference between nodes being too small to determine its importance.In this paper,a new centrality measurement method is proposed to measure the importance of multilayer networks by calculating their weighted local structural entropy.This method not only considers the importance of connections within the node layer,but also increases the influence of centrality of the network layer the node belongs to and the number of network layers the node connects to.Through the empirical analysis of Hubei three-layer traffic network,Lazega-Law-Firm multilayer network,CS-Aarhus multilayer network,CKM-Physician-Innovation multilayer network,and compare with the existing multilayer network node centrality method,such as degree centrality,random walking between centrality,closeness centrality and other five node centrality measurement methods.The empirical results show that the proposed method can accurately identify the central nodes that play an important role in information interaction and transmission in multilayer networks,and has the advantages of accuracy and effectiveness,strong universality and low computational complexity.(2)Considering the global characteristics of multilayer networks,a measurement model of interlayer correlation of multilayer networks is constructed.The interaction between layers in a multilayer network will generate new structural features.The most prominent feature is link overlap between layers,that is,the existence of links in one layer of the network is related to the existence of links in the other layer.This paper focuses on how to analyze the relationship between the structure interaction between the composite layers and the network behavior.Based on the information fusion theory of evidence theory,this paper constructs a measure model of interlayer correlation.Combining information fusion entropy and overlapping links between combined layers in multilayer networks to quantify the interlayer correlation of networks.Through the empirical measurement of CSAarhus multilayer network,Tailor-shop multilayer network,C.elegans multilayer network and 7thGraders multilayer network,the results show that the measurement results of interlayer correlation are corresponding to the correlation behavior of interlayer network.It is also proved that the more layers of the network,the more difficult the coupling between the composite layers to achieve consistency,the more unstable the system.This paper mainly studies the structural characteristics of multilayer networks from two perspectives: local(node centrality)and global(interlayer correlation).The research results not only enrich the existing theories of the structural characteristics of multilayer networks,but also provide a reference for the subsequent research on the structure and dynamics of multilayer networks.