  We propose a simple model that aims at describing, in a stylized manner, how
local breakdowns due unbalances or congestion propagate in real dynamical
networks. The model converges to a self-organized critical stationary state in
which the network shapes itself as a consequence of avalanches of rewiring
processes. Depending on the model's specification, we obtain either single
scale or scale-free networks. We characterize in detail the relation between
the statistical properties of the network and the nature of the critical state,
by computing the critical exponents. The model also displays a non-trivial,
sudden, collapse to a complete network.
