Title: Node classification for signed networks using diffuse interface methods,
Abstract: Signed networks are a crucial tool when modeling friend and foe
relationships. In contrast to classical undirected, weighted graphs, the edge
weights for signed graphs are positive and negative. Crucial network properties
are often derived from the study of the associated graph Laplacians. We here
study several different signed network Laplacians with a focus on the task of
classifying the nodes of the graph. We here extend a recently introduced
technique based on a partial differential equation defined on the signed
network, namely the Allen-Cahn-equation, to classify the nodes into two or more
classes. We illustrate the performance of this approach on several real-world
networks.