  We present an evolving network model in which the total numbers of nodes and
edges are conserved, but in which edges are continuously rewired according to
nonlinear preferential detachment and reattachment. Assuming power-law kernels
with exponents alpha and beta, the stationary states the degree distributions
evolve towards exhibit a second order phase transition - from relatively
homogeneous to highly heterogeneous (with the emergence of starlike structures)
at alpha = beta. Temporal evolution of the distribution in this critical regime
is shown to follow a nonlinear diffusion equation, arriving at either pure or
mixed power-laws, of exponents -alpha and 1-alpha.
