In this paper, we will study the geometric structure on the Sierpinski networks which are skeleton networks of a connected self-similar Sierpinski carpet. Under some suitable condition, we figure out that the renormalized shortest path distance is comparable to the planar Manhattan distance, and obtain the Hausdorff dimension of Sierpinski networks.

中文翻译：

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谢尔宾斯基网络的最短路径距离和Hausdorff维数

在本文中，我们将研究谢尔宾斯基网络的几何结构，谢尔宾斯基网络是连接的自相似谢尔宾斯基地毯的骨架网络。在一定条件下，我们发现重整化最短路径距离与平面曼哈顿距离相当，并得到了Sierpinski网络的Hausdorff维数。