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

TL;DR

This paper introduces a steady state network model that produces 1/k scale-free degree distributions through node duplication and deletion, without network growth, balancing preferential attachment and detachment.

Contribution

It presents a novel steady state model generating 1/k scale-free networks without growth, supported by mean field analysis and simulations.

Findings

Networks exhibit 1/k degree distribution in steady state.

Distributional forms vary when perfect duplication is relaxed.

Model matches simulation data under certain approximations.

Abstract

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.