复杂网络的Farey图模型
Farey Graphs as Models for Complex Networks
摘要：
0和1之间的不可约分数的Farey序列可以与称为Farey图的图构造相关。这些图首先由Matula和Kornerup在1979年提出，并由Colbourn在1982年进一步研究，它们具有许多有趣的性质：它们是极小3-可着色的，唯一Hamilton的，极大外平面的和完美的。在本文中，我们介绍了一个简单的生成方法的Farey图的家庭，我们研究分析相关的拓扑性质：秩序，大小，度分布和相关性，聚类，传递性，直径和平均距离。我们表明，图是一个很好的模型与一些复杂系统的网络。
英文摘要：
Farey sequences of irreducible fractions between 0 and 1 can be related to graph constructions known as Farey graphs. These graphs were first introduced by Matula and Kornerup in 1979 and further studied by Colbourn in 1982 and they have many interesting properties: they are minimally 3-colorable, uniquely Hamiltonian, maximally outerplanar and perfect. In this paper we introduce a simple generation method for a Farey graph family, and we study analytically relevant topological properties: order, size, degree distribution and correlation, clustering, transitivity, diameter and average distance. We show that the graphs are a good model for networks associated with some complex systems.
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