Maximal planar scale-free Sierpinski networks with small-world effect and power law strength-degree correlation

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

Corresponding authors: zhangzz@fudan.edu.cn sgzhou@fudan.edu.cn

Received: 3 May 2007
Accepted: 19 June 2007

Abstract

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.