Journal of Applied Mathematics
Volume 2013 (2013), Article ID 902519, 6 pages
Research Article

Exact Solutions of a Generalized Weighted Scale Free Network

1School of Mathematics and Statistics, Central South University, Changsha, Hunan 410075, China
2School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan 410075, China

Received 7 September 2012; Revised 9 January 2013; Accepted 6 February 2013

Academic Editor: Constantinos Siettos

Copyright © 2013 Li Tan and Dingyou Lei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate a class of generalized weighted scale-free networks, where the new vertex connects to m pairs of vertices selected preferentially. The key contribution of this paper is that, from the standpoint of random processes, we provide rigorous analytic solutions for the steady state distributions, including the vertex degree distribution, the vertex strength distribution and the edge weight distribution. Numerical simulations indicate that this network model yields three power law distributions for the vertex degrees, vertex strengths and edge weights, respectively.