Scale-free networks without growth

Details Scale-free networks without growth Scale-free networks without growth

2005-12-20

arxiv.org/abs/cond-mat/0512485v1

Physica A 387, 1683-1688 (2008)

Physics

Condensed Matter

Statistical Mechanics

4 pages and 3 figures

Scientific paper

In this letter, we proposed an ungrowing scale-free network model, wherein the total number of nodes is fixed and the evolution of network structure is driven by a rewiring process only. In spite of the idiographic form of $G$, by using a two-order master equation, we obtain the analytic solution of degree distribution in stable state of the network evolution under the condition that the selection probability $G$ in rewiring process only depends on nodes' degrees. A particular kind of the present networks with $G$ linearly correlated with degree is studied in detail. The analysis and simulations show that the degree distributions of these networks can varying from the Possion form to the power-law form with the decrease of a free parameter $\alpha$, indicating the growth may not be a necessary condition of the self-organizaton of a network in a scale-free structure.

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