基于Ammann-Beenker拼图的复杂网络的模型构造与统计性质

Modeling and Statistical Properties of Complex Networks Based on Ammann-Beenker Tiling

摘要: 作为八次旋转对称结构的Ammann-Beenker拼图，在准晶体的研究中占用重要的地位。本文采用自相似变化法得到Ammann-Beenker拼图，研究该拼图对应的规则复杂网络以及加入随机连接演化出的网络的统计性质，主要包括度分布，度关联和集群系数等。本工作为复杂网络与准周期结构相结合的研究提供了一种新的途径。

Abstract: As an eight-fold symmetric structure, the Ammann-Beenker tiling plays an important role in qua-sicrystal study. We generate the Ammann-Beenker tiling by self-similar transformation and inves-tigate the statistical properties of the corresponding regular complex network and the evolved complex network by adding random connections. The properties include the degree distribution, degree correlation and cluster coefficient. This work suggests a new approach to combine the qu-asicrystal structure and the complex network.