| 一类具有分形和小世界特性的网络图 |
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| 引用本文： | 那日萨,张书超,穆青.一类具有分形和小世界特性的网络图[J].系统工程,2007,25(3):115-119. |
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| 作者姓名： | 那日萨 张书超 穆青 |
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| 作者单位： | 1. 大连理工大学,系统工程研究所,辽宁,大连,116023
2. 大连理工大学,数学系,辽宁,大连,116024 |
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| 摘 要： | 提出一类具有分形和小世界特性的网络图.利用数学归纳的方法计算出了网络图的集聚系数,平均最短路径和网络图的直径,证明了网络图的小世界特性.用盒维数和豪斯道夫维数来衡量网络图的分形性,得到其维数均为1.585.最后对网络图的构造方法作了进一步地拓展,并给出了拓展的网络图的相关拓扑特性的表达式,并认为其和原来的网络图可归结为一类具有分形和小世界特性的网络图.
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| 关 键 词： | 复杂网络 分形 小世界 复杂系统 |
| 文章编号： | 1001-4098（2007）03-0115-05 |
| 修稿时间： | 2007-01-06 |
A Class of Graphs with Fractality and Small-world Effect |
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| ZHAO Narisa,ZHANG Shu-chao,MU Qing.A Class of Graphs with Fractality and Small-world Effect[J].Systems Engineering,2007,25(3):115-119. |
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| Authors: | ZHAO Narisa ZHANG Shu-chao MU Qing |
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| Institution: | 1. Institute of System Engineering, Dalian University of Technology,Dalian 116023,China ; 2.Department of Mathematics and Applied Mathematics, Dalian University of Technology,Dalian 116024,China |
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| Abstract: | In this paper, we propose a class of graphs with fractality and small-world effect. The clustering coefficient, the average length of the graphs, and the diameter are calculated analytically. Also we calculate the box-counting dimension and Hausdorff dimension as a measure of their fractality and the value of the dimension is 1. 585. At last, the method of the constructing graphs is expanded, and the expressions of the relevant characteristics of the expanded graphs are given. The expanded graphs and the graphs proposed before are considered as a class of graphs with fractality and small-world effect. |
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| Keywords: | Complex Networks Fractality Small-world Complex Systems |
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