Abstract
Using a steady-state process of node duplication and deletion, relevant to biological and ecological systems, we produce networks with 1/k scale-free degree distributions in the limit of vanishing connectance. The process involves no growth in nodes 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 also arise when the duplication fidelity is relaxed.