Many real complex networks behave similarly with the scale-free and the small-world properties. In this paper, we create a special hierarchical network with the Fibonacci word. This network is self-similar on some scales due to Fibonacci word’s recurrence property. Based on the construction of the graph, we study the clustering coefficient, the average path length and the cumulative degree distribution of our network. These results show the scale-free and the small-world effects of the evolving network. Moreover, the monotony of the standardized average path length and the average clustering coefficient is coincided with that of the Fibonacci word by applying the balance property of the Sturmian word. We think the Sturmian word can be an useful tool to describe some complex networks.

许多真实的复杂网络在无标度和小世界特性下的行为类似。在本文中，我们使用斐波那契词创建一个特殊的分层网络。由于斐波那契单词的递归特性，该网络在某些规模上是自相似的。基于图的构造，我们研究了网络的聚类系数，平均路径长度和累积度分布。这些结果显示了不断发展的网络的无标度和小世界效应。而且，通过应用Sturmian单词的平衡特性，标准化平均路径长度和平均聚类系数的单调与Fibonacci单词的单调一致。我们认为Sturmian单词可能是描述某些复杂网络的有用工具。