Partition signed social networks by spectral features and structural balance

In social networks, individuals are usually but not exactly divided into communities such that within each community people are friendly to each other while being hostile towards other communities. This is in line with structural balance theory which enables a comprehensive understanding of the stability and tensions of social systems. Yet, there may be some conflicts such as the intra-community negative edges or inter-community positive edges that affect the balancedness of the social system. This raises an interesting question of how to partition a signed network for minimal conflicts, i.e., maximum balancedness. In this paper, by analyzing the relationship between balancedness and spectrum space, we find that each eigenvector can be an indicator of dichotomous structure of networks. Incorporating the leader mechanism, we partition signed networks to maximize the balancedness with top-k eigenvectors. Moreover, we design an optimizing segment to further improve the balancedness of the network. Experimental data both from real social and synthetic networks demonstrate that the spectral algorithm has higher efficiency, robustness and scientificity.