  We study the evolution of social networks that contain both friendly and
unfriendly pairwise links between individual nodes. The network is endowed with
dynamics in which the sense of a link in an imbalanced triad--a triangular loop
with 1 or 3 unfriendly links--is reversed to make the triad balanced. With this
dynamics, an infinite network undergoes a dynamic phase transition from a
steady state to "paradise"--all links are friendly--as the propensity p for
friendly links in an update event passes through 1/2. A finite network always
falls into a socially-balanced absorbing state where no imbalanced triads
remain. If the additional constraint that the number of imbalanced triads in
the network does not increase in an update is imposed, then the network quickly
reaches a balanced final state.
