  We introduce a spectral embedding algorithm for finding proximal
relationships between nodes in signed graphs, where edges can take either
positive or negative weights. Adopting a physical perspective, we construct a
Hamiltonian which is dependent on the distance between nodes, such that
relative embedding distance results in a similarity metric between nodes. The
Hamiltonian admits a global minimum energy configuration, which can be
reconfigured as an eigenvector problem, and therefore is computationally
efficient to compute. We use matrix perturbation theory to show that the
embedding generates a ground state energy, which can be used as a statistical
test for the presence of strong balance, and to develop an energy-based
approach for locating the optimal embedding dimension. Finally, we show through
a series of experiments on synthetic and empirical networks, that the resulting
position in the embedding can be used to recover certain continuous node
attributes, and that the distance to the origin in the optimal embedding gives
a measure of node extremism.
