Clusters detection based leading eigenvector in signed networks

Abstract The structural balance theory offers a comprehensive way to understand stability and tensions in social systems. However, most of the real social networks are unbalanced in which people are not exclusively divided into groups such that people within a group are friendly to each other but hostile to everyone in other groups. That is, there are conflict edges in a partition regardless of how we divide people in a given social network. The natural question to ask is that how many conflict edges should be changed to make a network balanced. Alternatively, the clustering problem is formulated to optimize minimum conflicts or maximum balanceness. In this paper, utilizing the relationship between balancedness and spectrum space, we propose a spectral algorithm based leading eigenvectors of signed networks to partition clusters and make balancedness maximum. The spectral algorithm is a two stages approach, partition subnetworks corresponding to temporary clusters to increase the objective value and fine-tune partition based on the fitness of nodes. The robustness of the algorithm is completely dependent on the adjacent matrixes of signed networks. And it can measure the balanceness of network in global way with the lowest errors. The experimental results on both real signed networks and synthetic networks demonstrate that the leading eigenvector based method is highly effective and accuracy.

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