Quantitative Measures In Multilayer Information Networks

With the continuous development of informetrics,information network analysis has become an important research area.Traditional research about monolayer information network and bipartite information network has become mature,their research scope covered various entities and their relationships of academic information network.Traditional information network modeling often only consider a kind of node,a kind of relationship between nodes,or two kinds of nodes,a kind of relationship between nodes,and did not involve a kind of node,multiple kinds of relationship between nodes or multiple kinds of node,multiple kinds of relationship between nodes.However,the real information network is complex heterogeneous information network space with various types of nodes and various types of relationships.Over the past four years,mathematical modeling and node importance measure of the multilayer network has obtained some research results in the field of network science.This paper will consider some practical problems in the field of library and information science,using multilayer network modeling theory,to set up the core structure measure,and to propose the core structure measure system framework of multilayer information network.In this paper,the concept of multilayer information network is proposed under the background of continuous evolution of information network;the main concept types of multilayer information network are defined;the mathematical model,formal definition,representation mode,storage format,and computing model are constructed;the calculation tools and common indexes are studied;two examples of undirected weighted multilayer information network and directed weighted multilayer information network are collected and collated.In the two cases of multilayer information network,the following four core structure measurement methods are adopted:(1)Proposing h-crystal core structure construction method in the multilayer information network.Based on the h-degree and the h-strength of the monolayer information network,the subnetwork structure such as network h-core and h-subnet of the weighted information network is constructed,and the h-type measure methods in the undirected weighted information network are extended to the directional weighted information network.In the two instances of the multilayer information network,the h-crystal of the multilayer information network is constructed by the relevant h-type measure methods.The characteristics and correlations of the points and edges in h-crystal are analyzed and compared.The significance of the h-crystal core structure is confirmed.(2)Proposing motif hirsch subgraphs core structure construction method in the multilayer information network.Based on the motif hirsch subgraphs construction method in the undirected information network,the motif hirsch subgraphs measure is extended to the weighted information network by using the motif measure of the directed information network and considering the weight of the motif.In the two instances of the multilayer information network,the motif hirsch subgraphs of the multilayer information network is constructed by the motif hirsch subgraphs method.The characteristics and correlations of the points and edges in the motif hirsch subgraphs are analyzed and compared.The significance of the motif hirsch subgraphs core structure is confirmed.(3)Proposing s-core core structure construction method in the multilayer information network.Mainly based on the k-core algorithm in the monolayer information network,the s-core algorithm in the weighted information network,the D-core algorithm in the directional information network,and the(k1,k2)-core algorithm in the multiplex network,the s-core of the multilayer information network is constructed by the s-core measure method in the two instances of the multilayer information network.The characteristics and correlations of the points and edges in the s-core are analyzed and compared.The significance of the s-core core structure is confirmed.(4)Proposing t-core core structure construction method in the multilayer information network.Mainly considerating the number and intensity of strongly connected triangle structure in information network,the t-core structure of the undirected or directed weighted information network is constructed.In the two instances of the multilayer information network,the t-core of the multilayer information network is constructed by the t-core method.The characteristics and correlations of the points and edges in the t-core are analyzed and compared.The significance of the t-core core structure is confirmed.Finally,the comparison of h-crystal,motif hirsch subgraphs,s-core and t-core of multilayer information network is carried out.Compared with node number,edge number,node maximum degree,node average degree,node maximum strength,node average strength,connectivity,network diameter,average shortest path length,average degree centrality,mean closeness centrality,average betweenness centrality,network structure entropy,and so on,which show that these four measures are significant differences,can complement each other.