The Study Of Two Complex Network Community Measure Metrics

In recent years,with the in-depth study of complex networks,more and more systems can be abstracted into complex networks for research.For example,intricate routes constructed the airline network,and the interpersonal relationships constitute the social network.Because there are many types of complex networks and the network structures characteristics are not the same for the different sizes and types of networks,which have led to many methods for studying the multidisciplinary and multidisciplinary subject of complex networks.Among them,the study of the network community structure has become a hotspot issue in the current.At present,the study of community structure includes two main directions,one is the theory and algorithm of community division,and the other is the property of the community.In the research of community property,how to construct the metrics of community nature is an open insure,in this paper,community measurement indexes are studied.Based on the structure entropy,critical state function,and other theories,two new measures are proposed.Moreover,the community structure of constructed complex networks and real networks are measured by the proposed method.The results show the rationality of these metrics.The main contributions of this paper are as follows:1.The measure index of the community complexity is established based on the structure entropy.Not only the structure complexity within the community but also the complexity among the communities is also considered.On the one hand,the degree and betweenness are fused in the nonextensive entropy,and combination with absolute density,it is used to measure the complexity of the internal structure of the community.On the other hand,the amount of information between nodes among communities and the similarity of neighbor nodes is used to measure the complexity among communities.2.Based on the critical state function,the metrics of the community influence is set up.By improving the classic renormalization method,the clustering coefficient within the community and the edges among communities are considered as weights in the renormalization process.At the same time,the community structure is converted to a weighted network by the renormalization method.The idea of critical state function to identify the importance of nodes is used to measure the influence of the corresponding community.3.The two proposed methods are applied to measure the community structure complexity and influence of constructed networks,that is,four small-world networks,scale-free networks,random networks,and actual networks,and real networks(i.e.the 9/11 terrorist organization networks,USAirlines networks,protein interaction network,C.elegans network,U.S.electric power network,and U.S.political network).The results show that the proposed methods are effective in the constructed networks and real networks,which are useful for studying disaster prevention and network structure analysis in real life.