In this paper, the evolving networks are created from a series of Sierpinski-type polygon by applying the encoding method in fractal and symbolic dynamical system. Based on the self-similar structures of our networks, we study the cumulative degree distribution, the clustering coefficient and the standardized average path length. The power-law exponent of the cumulative degree distribution is deduced to be [Formula: see text] and the average clustering coefficients have a uniform lower bound [Formula: see text]. Moreover, we find the asymptotic formula of the average path length of our proposed networks. These results show the scale-free and the small-world effects of these networks.

中文翻译：

---

谢尔宾斯基型多边形上的分形网络

本文采用分形和符号动力系统中的编码方法，从一系列谢尔宾斯基型多边形中创建演化网络。基于我们网络的自相似结构，我们研究了累积度分布、聚类系数和标准化平均路径长度。推导出累积度分布的幂律指数为[公式：见正文]，平均聚类系数有一个统一的下界[公式：见正文]。此外，我们找到了我们提出的网络的平均路径长度的渐近公式。这些结果显示了这些网络的无标度和小世界效应。