On Spectral Analysis of Signed and Dispute Graphs

This paper presents a spectral analysis of signed networks from both theoretical and practical aspects. On the theoretical aspect, we conduct theoretical study based on matrix perturbation theorem for analyzing community structures of complex signed networks and show how the negative edges affect distributions and patterns of node spectral coordinates in the spectral space. We prove and demonstrate cluster orthogonality for two types of signed networks: graph with dense inter-community mixed sign edges and k-dispute graph. We show why the line orthogonality pattern does not hold in the spectral space for these two types of networks. On the practical aspect, we have developed a clustering method to study signed networks and k-dispute networks. Empirical evaluations on both synthetic and real networks show our algorithm outperforms existing clustering methods on signed networks in terms of accuracy.