https://doi.org/10.1140/epjb/e2013-40246-5
Regular Article
Efficiency of transportation on weighted extended Koch networks
1 Business School, University of
Shanghai for Science and Technology, Shanghai
200093, P.R.
China
2 Department of Mathematics, Shanghai
University, Shanghai
200444, P.R.
China
a
e-mail: zhanghongjuan@shu.edu.cn
Received:
24
March
2013
Received in final form:
4
July
2013
Published online:
1
October
2013
In this paper, we propose a family of weighted extended Koch networks based on a class of extended Koch networks. They originate from a r-complete graph, and each node in each r-complete graph of current generation produces mr-complete graphs whose weighted edges are scaled by factor h in subsequent evolutionary step. We study the structural properties of these networks and random walks on them. In more detail, we calculate exactly the average weighted shortest path length (AWSP), average receiving time (ART) and average sending time (AST). Besides, the technique of resistor network is employed to uncover the relationship between ART and AST on networks with unit weight. In the infinite network order limit, the average weighted shortest path lengths stay bounded with growing network order (0 < h < 1). The closed form expression of ART shows that it exhibits a sub-linear dependence (0 < h < 1) or linear dependence (h = 1) on network order. On the contrary, the AST behaves super-linearly with the network order. Collectively, all the obtained results show that the efficiency of message transportation on weighted extended Koch networks has close relation to the network parameters h, m and r. All these findings could shed light on the structure and random walks of general weighted networks.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2013