Maximal planar scale-free Sierpinski networks with small-world effect and power law strength-degree correlationZhongzhi Zhang1, 2, Shuigeng Zhou1, 2, Lujun Fang1, 2, Jihong Guan3 and Yichao Zhang4
1 Department of Computer Science and Engineering, Fudan University - Shanghai 200433, China
2 Shanghai Key Lab of Intelligent Information Processing, Fudan University - Shanghai 200433, China
3 Department of Computer Science and Technology, Tongji University - 4800 Cao'an Road, Shanghai 201804, China
4 School of Material and Engineering, Shanghai University - Shanghai 200072, China
received 3 May 2007; accepted in final form 19 June 2007; published August 2007
published online 16 July 2007
Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski networks, which are induced by the famous Sierpinski fractals and constructed in a simple iterative way. We derive analytical expressions for degree distribution, strength distribution, clustering coefficient, and strength-degree correlation, which agree well with the characterizations of various real-life networks. Moreover, we show that the introduced Sierpinski networks are maximal planar graphs.
89.75.Da - Systems obeying scaling laws.
05.45.Df - Fractals.
02.10.Ox - Combinatorics; graph theory.
© Europhysics Letters Association 2007