Spanning trees in a fractal scale-free lattice.
Spanning trees in a fractal scale-free lattice.
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DOI：
10.1103/physreve.83.016116
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Zhongzhi Zhang;Hongxiao Liu;Bin Wu;Tao Zou
中科院分区：
文献类型：
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作者：
Zhongzhi Zhang;Hongxiao Liu;Bin Wu;Tao Zou
生成树为分形无标度网络中分形的起源提供了重要的见解。在本文中，我们提出了一个特殊的分形无标度格（网络）的生成树的数量。我们首先研究分析晶格的拓扑特征，并表明它同时是无标度的，高度聚集的，“大世界”，分形，和dispertative。任何以前的模型都不具有所研究的模型的所有属性。然后，通过使用重整化群技术，我们解析地推导出所考虑的网络中的生成树的数量，并在此基础上确定网络的生成树的熵。这些结果对于理解分形无标度网络的结构特征和动力学过程具有重要意义。此外，我们的方法和过程采用抽取技术枚举生成树是通用的，可以很容易地扩展到其他确定性介质的自相似性。
Spanning trees provide crucial insight into the origin of fractality in fractal scale-free networks. In this paper, we present the number of spanning trees in a particular fractal scale-free lattice (network). We first study analytically the topological characteristics of the lattice and show that it is simultaneously scale-free, highly clustered, "large-world," fractal, and disassortative. Any previous model does not have all the properties as the studied one. Then, by using the renormalization group technique we derive analytically the number of spanning trees in the network under consideration, based on which we also determine the entropy for the spanning trees of the network. These results shed light on understanding the structural characteristics of and dynamical processes on scale-free networks with fractality. Moreover, our method and process for employing the decimation technique to enumerate spanning trees are general and can be easily extended to other deterministic media with self-similarity.