Europhys. Lett.
Volume 76, Number 4, November 2006
Page(s) 731 - 737
Section Interdisciplinary physics and related areas of science and technology
Published online 18 October 2006
Europhys. Lett., 76 (4), pp. 731-737 (2006)
DOI: 10.1209/epl/i2006-10315-2

Degree distributions of evolving networks

D. Shi1, L. Liu2, S. X. Zhu3 and H. Zhou4

1  Department of Mathematics, Shanghai University - Shanghai 200444, PRC
2  Department of Logistics, Hong Kong Polytechnic University - Hung Hom, Hong Kong
3  Department of Information and Systems Management, Hong Kong University of Science and Technology - Clear Water Bay, Hong Kong
4  College of Science and Technology, Ningbo University - Ningbo 315211, PRC

received 20 June 2006; accepted in final form 22 September 2006
published online 18 October 2006

In this paper, we propose a simple evolving network model with link and node removals as well as additions and show that this evolving network is scale free with a degree exponent varying in (1,4] depending on the network parameter values. By establishing a relation between the network evolution and a set of non-homogeneous birth-and-death processes, we develop an efficient algorithm to compute the network degree distribution. Our numerical results match simulation well and show how the network evolves into the scale-free state.

89.75.Hc - Networks and genealogical trees.
64.60.Fr - Equilibrium properties near critical points, critical exponents.
87.23.Ge - Dynamics of social system.

© EDP Sciences 2006