Projecting Signed Two-mode Networks

Signed two-mode networks have so far predominantly been analysed
using blockmodeling techniques. In this work, we put forward the idea
of projecting such networks onto its modes. Two projection methods
are introduced which allow the application of known dichotomization
tool for weighted networks to obtain a simple signed network. It turns
out, however, that resulting networks may contain ambivalent ties, de
fined as conjunctions of positive and negative ties. We show that this
requires the reformulation of matrices related to the network and in
troduce the complex adjacency and Laplacian matrix. These matrices
are used to prove some properties related to balance theory including
ambivalence.