We study the application of spectral clustering, prediction and visualization methods to graphs with negatively weighted edges. We show that several characteristic matrices of graphs can be extended to graphs with positively and negatively weighted edges, giving signed spectral clustering methods, signed graph kernels and network visualization methods that apply to signed graphs. In particular, we review a signed variant of the graph Laplacian. We derive our results by considering random walks, graph clustering, graph drawing and electrical networks, showing that they all result in the same formalism for handling negatively weighted edges. We illustrate our methods using examples from social networks with negative edges and bipartite rating graphs.
Kunegis et al. REF study the spectral properties of signed networks and use kernels derived from a signed variant of the graph Laplacian for link prediction.
Spectral Analysis of Signed Graphs for Clustering, Prediction and Visualization
SDM
Computer Science