Modeling And Empirical Analysis Of Multi-layer Complex Networks

In recent years,due to the continuous innovation and development of Internet technology,the network in reality emerges one after another,and the study of complex network has attracted widespread attention of scholars in many fields.We can come into contact with all kinds of networks in our daily life,such as the power network formed by national transmission lines,the protein interaction network in life science,the social network in online social media,the food chain network in biological science,and so on.These real networks can be modeled and analyzed using complex networks.With the accumulation of practical network models and properties,it is found that many networks have multi-level and cluster structure,especially some large-scale networks are usually composed of multiple interrelated subnetworks,which are called multi-layer networks.For example,the interpersonal network can be viewed as a combination of online and offline social networks;Transportation network is composed of air network,land traffic network and water transport network.Therefore,the research of multilayer complex network has a wide range of practical background and application value.In this paper,the modeling and analysis method of multi-layer complex network is mainly applied to carry out multi-layer network modeling and empirical analysis on two groups of actual network data.The specific research contents are as follows:Model construction and analysis method of multi-layer network.Firstly,several types of multi-layer complex network models are summarized,including multiple network,time network,interaction network and interdependence network.Secondly,three common multi-layer network construction methods are described.Multi-layer network can be constructed by matrix expression,aggregate network or tensor.Finally,the relevant index statistics for analyzing the multi-layer network topology are given.The main indexes include degree sequence,overlap degree,participation coefficient and node entropy of network nodes.The correlation index of the overlap between layers and the interlayer degree of the network,etc.These methods and indicators are the basis for us to build multi-layer network model for actual data.The study of relevant statistical indicators is helpful for us to better understand the multi-layer network structure of real complex system,and further analyze and mine the deep network information.Secondly,the multi-layer network modeling and empirical analysis are carried out for two sets of actual data sets.In this paper,two sets of data sets,the Aarhus five-tier network and the European 37-tier route network,are selected as the research objects,and the corresponding multi-tier network models are established respectively according to the data sets.The topological properties of two multi-layer networks are analyzed through the related indexes of the network,including the similarity and overlap between the node properties of each node and the sub-layer networks,and the active nodes and important sub-layers of the network are further excavated.Through empirical analysis,we find that:(1)Both the two empirical networks conform to the characteristics of scale-free networks;(2)The sub-layer network of Aarhus social network has obvious small-world effect;(3)In Aarhus social network,the working layer and the lunch layer have the highest similarity;(4)There is a high correlation between the sublayer networks of airlines belonging to the same country in the European route network.These network topological information reflect some characteristics of interpersonal relationship or airline relationship in actual company system or aviation system,which can provide reference for relevant managers to formulate management or control measures.