On Spectral Analysis of Signed and Dispute Graphs: Application to Community Structure - 2017


This paper presents a spectral analysis of signed networks from both theoretical and practical aspects. On the theoretical facet, we conduct theoretical studies based on results from matrix perturbation for analyzing community structures of advanced signed networks and show how the negative edges affect distributions and patterns of node spectral coordinates within the spectral area. We tend to prove and demonstrate that node spectral coordinates type orthogonal clusters for two varieties of signed networks: graphs with dense inter-community mixed sign edges and k -dispute graphs where inner-community connections are absent or very sparse but inter-community connections are dense with negative edges. The cluster orthogonality pattern is totally different from the road orthogonality pattern (i.e., node spectral coordinates kind orthogonal lines) observed within the networks with k -block structure. We have a tendency to show why the line orthogonality pattern does not hold in the spectral area for these 2 varieties of networks. On the sensible facet, we tend to have developed a clustering method to check signed networks and k -dispute networks. Empirical evaluations on both synthetic networks (with up to 1 million nodes) and real networks show our algorithm outperforms existing clustering methods on signed networks in terms of accuracy and potency.

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