  We model a close-knit community of friends and enemies as a fully connected
network with positive and negative signs on its edges. Theories from social
psychology suggest that certain sign patterns are more stable than others. This
notion of social "balance" allows us to define an energy landscape for such
networks. Its structure is complex: numerical experiments reveal a landscape
dimpled with local minima of widely varying energy levels. We derive rigorous
bounds on the energies of these local minima and prove that they have a modular
structure that can be used to classify them.
