On Spectral Analysis of Directed Signed Graphs
This work addresses a gap in network analysis for researchers studying directed signed graphs, though it appears incremental as it extends existing spectral methods to a new graph type.
The paper tackles the lack of spectral analysis for directed signed graphs by deriving theoretical approximations of spectral projections using matrix perturbation theory and developing a spectral clustering algorithm, SC-DSG, which is shown to be effective in evaluations on synthetic and real datasets.
It has been shown that the adjacency eigenspace of a network contains key information of its underlying structure. However, there has been no study on spectral analysis of the adjacency matrices of directed signed graphs. In this paper, we derive theoretical approximations of spectral projections from such directed signed networks using matrix perturbation theory. We use the derived theoretical results to study the influences of negative intra cluster and inter cluster directed edges on node spectral projections. We then develop a spectral clustering based graph partition algorithm, SC-DSG, and conduct evaluations on both synthetic and real datasets. Both theoretical analysis and empirical evaluation demonstrate the effectiveness of the proposed algorithm.