A steady state network model with a 1/k scale-free degree distribution

摘要

Using a steady state process of node duplication and deletion we producenetworks with 1/k scale-free degree distributions in the limit of vanishingconnectance. This occurs even though there is no growth involved and inherentpreferential attachment is counterbalanced by preferential detachment. The meanfield evolution is considered and the 1/k law is verified under certainapproximations. An ansatz for the degree distribution is proposed on the basisof symmetry considerations and is shown to coincide well with the simulationdata. Distributional forms other than power law are also shown to arise whenthe condition of perfect duplication is relaxed.