关键词: 社会网络, 相似性, 集对, 同异反关系, 社区发现

Abstract: Set pair analysis as the mathematical theory of dealing with the interaction system of certainty and uncertainty, can be used to deal with the complexity social network of uncertain relationship. Firstly, based on the application of set pair analysis theory, this paper takes social network as an identical-different-contrary system (certain and uncertain system). Based on set pair connection degree to descript the identical, different and contrary relations between vertices, considering the contribution of local features and the topological structure to the vertex similarity, this paper defines the similarity between vertices based on the relation connection degree taking into account weight and clustering coefficient. The measurement can better describe network structure characteristics, overcome the under-estimating for some similarity between vertices based on traditional local structures, and reduce the computational complexity of global similarity indices. Secondly, in order to utilize the similarity indices to community discovering, combined with agglomerative hierarchical clustering algorithm, it is applicable to detect community structures in complex networks with any object that has similarity measurement. Finally, through the experiment of community mining on the social network, and compared with the typical algorithms of community discovering, the experimental results verify the correctness and effectiveness of the similarity measurement.

Key words: social network, similarity, set pair, identical-different-contrary relations, community discovering