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.