  Using a steady state process of node duplication and deletion we produce
networks with 1/k scale-free degree distributions in the limit of vanishing
connectance. This occurs even though there is no growth involved and inherent
preferential attachment is counterbalanced by preferential detachment. The mean
field evolution is considered and the 1/k law is verified under certain
approximations. An ansatz for the degree distribution is proposed on the basis
of symmetry considerations and is shown to coincide well with the simulation
data. Distributional forms other than power law are also shown to arise when
the condition of perfect duplication is relaxed.
