Signed Graph Balancing with Graph Cut

Signed graphs–graphs with both positive and negative edge weights–are useful to specify pairwise dissimilarities as well as similarities in data. However, unlike graph variation operators (e.g., adjacency and graph Laplacian matrices) for unsigned graphs, the spectra of signed graph variation operators are not well understood in general. The lone exception is balanced signed graphs: there exists a one-to-one mapping of eigen-pairs between a balanced signed graph and its corresponding unsigned positive graph, which means that spectral filters for well-studied positive graphs can be reused if signed graphs are balanced. In this paper, we propose a simple yet effective method to balance a signed graph. Specifically, we balance a signed graph by removing carefully chosen edges, while the cuts of positive / negative edges are minimized / maximized, respectively. Experimental results on graph signal denoising and interpolation show that our signed graph balancing algorithms achieved promising results.