Study On The Measure Methods Of Similarity Between Vertices In Networks

The new online social media,such as Facebook,Twitter,We Chat and Micro-Blog,as the band between the real world and the virtual space,bringing together a large number of human society digital footprints,such as relation and behavior,which can be perceived and calculated.With the expansion of network scale,the research on the social network analysis has become a hot spot,and aroused much concern of many scholars.The measure methods of similarity between vertices as the basis of social network analysis have important theoretical significance and practical value to the link prediction,community discovery,community evolution and influence maximization,ect.This paper introduces the set pair analysis theory,and depicts the social network as an identical-discrepancycontrary(certainty and uncertainty)system.It puts forward new similarity measure method,based on which social network is analyzed.The specific research contents are as follows.Firstly,in traditional social networks,there exist some problems in of similarity indices based on set pair analysis,for example they only consider the influence from the number of common neighbors,and ignore the influence of the network topological structure;thus,this paper proposes a new similarity index WCCD(Weighted Clustering-Coefficient Connection Degree).The index uses connection degree to describe the identical-discrepancy-contrary relation between vertices,and the relation is weighted by combines vertex features(such as degree,clustering coefficient,etc.)with networks topological structure.In order to verify the correctness and rationality of WCCD,the corresponding theorem and link prediction algorithm are given.Meanwhile,we propose a new community discovery algorithm based on WCCD,which can be used to reduce the frequent update operations in traditional hierarchical clustering algorithm,to avoid the unreasonable phenomenon of vertex clustering.Secondly,in signed networks,according to the existing problem of similarity indices,for example the complexity of many global methods are high,and the accuracy of the local ones is low as a result of vertices similarity underestimation;this paper proposes a new similarity index SNCD(Connection Degree Between Vertices in Signed Networks).To improve the accuracy of similarity,the index integrates the certain and uncertain relations in the signed networks,with the local and global network topology structure.In order to take into account the prediction accuracy of positive edges and negative edges,this paper proposes a new link prediction algorithm combining the clustering coefficient and structural balance theory.Meanwhile,we propose a new community evolution algorithm based on the prediction model in signed networks,which can improve the accuracy and stability of community partition,and can use the set pair theory to analyze the community evolution rules of signed networks.Finally,in topic attention networks,according to the characteristics of the two kinds entities,including user and subject,this paper proposes a new similarity index TANCD(Connection Degree Between Vertices in Topic Attention Networks).The index describes the identical-discrepancy-contrary relation between vertices,focuses on the user's attention of the topic,and highlights the importance of the topic in network structure.In order to accurately divide the topic-centered community,a community discovery algorithm based on TANCD is proposed.In order to achieve the maximization diffusion of the topic in networks,we propose the definition of topic preference and user influence,and the influence maximizing algorithm based on topic.