Europhys. Lett.
Volume 76, Number 4, November 2006
Page(s) 710 - 716
Section Interdisciplinary physics and related areas of science and technology
Published online 18 October 2006
Europhys. Lett., 76 (4), pp. 710-716 (2006)
DOI: 10.1209/epl/i2006-10319-x

A non-growth network model with exponential and $\mth{1/k}$ scale-free degree distributions

S. Laird and H. J. Jensen

Department of Mathematics, Imperial College London 180 Queen's Gate, London SW7 2AZ, UK

received 7 June 2006; accepted in final form 22 September 2006
published online 18 October 2006

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.

89.75.Fb - Structures and organization in complex systems.
89.75.Hc - Networks and genealogical trees.
87.23.Kg - Dynamics of evolution.

© EDP Sciences 2006