ABSTRACT
Almost all social networks model relationships as properties that are either non-existent, or have a positive intensity. In social networks so far, adjacency matrix entries are either zero or positive; a negative relationship can be modelled by a negative edge weight. This chapter describes an unnormalized Laplacian for signed graphs, and argues for the validity of the resulting construction based on both Rayleigh quotient and graph cut points of views. It shows the performance of all of the algorithms on real-world datasets from Epinions, Slashdot, and the Africa Armed Conflict Location & Event Data (ACLED), as well as two small datasets, the Gahuku-Gama alliance network of tribes in New Guinea, and the Sampson monastery network. The Sampson monastery dataset embeddings based on the three signed Laplacians. The ACLED is a dataset of political violence events in Africa from 1997 to the present.
