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

摘要

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 calledSierpinski networks, which are induced by the famous Sierpinski fractals andconstructed in a simple iterative way. We derive analytical expressions fordegree distribution, strength distribution, clustering coefficient, andstrength-degree correlation, which agree well with the characterizations ofvarious real-life networks. Moreover, we show that the introduced Sierpinskinetworks are maximal planar graphs.