  With a simple model, we study the evolution of random networks under attack
and reconstruction. We introduce a new quality, invulnerability I(s), to
describe the stability of the system. We find that the network can evolve to a
stationary state. The stationary value I_c has a power-law dependence on the
initial average degree <k>, with the slope is about -1.485. In the stationary
state, the degree distribution is a normal distribution, rather than a typical
Poisson distribution for general random graphs. The clustering coefficient in
the stationary state is much larger than that in the initial state. The
stability of the network depends only on the initial average degree <k>, which
increases rapidly with the decrease of <k>.
