Computational Biology and Machine Learning Laboratory, Center for Cancer Research and Cell Biology, School of Medicine, Dentistry and Biomedical Sciences, Faculty of Medicine, Health and Life Sciences, Queen's University Belfast, Belfast, United Kingdom.
PLoS One. 2013;8(2):e56461. doi: 10.1371/journal.pone.0056461. Epub 2013 Feb 19.
In this paper, we introduce a biologically inspired model to generate complex networks. In contrast to many other construction procedures for growing networks introduced so far, our method generates networks from one-dimensional symbol sequences that are related to the so called Collatz problem from number theory. The major purpose of the present paper is, first, to derive a symbol sequence from the Collatz problem, we call the step sequence, and investigate its structural properties. Second, we introduce a construction procedure for growing networks that is based on these step sequences. Third, we investigate the structural properties of this new network class including their finite scaling and asymptotic behavior of their complexity, average shortest path lengths and clustering coefficients. Interestingly, in contrast to many other network models including the small-world network from Watts & Strogatz, we find that CS graphs become 'smaller' with an increasing size.
在本文中，我们介绍了一种受生物启发的模型来生成复杂网络。与迄今为止引入的许多其他构建网络的过程不同，我们的方法从与数论中的 Collatz 问题相关的一维符号序列生成网络。本文的主要目的是，首先，从 Collatz 问题中推导出一个符号序列，我们称之为步序列，并研究其结构特性。其次，我们引入了一种基于这些步序列的网络生长构造过程。第三，我们研究了这种新的网络类的结构特性，包括它们的有限标度和复杂性、平均最短路径长度和聚类系数的渐近行为。有趣的是，与包括 Watts 和 Strogatz 的小世界网络在内的许多其他网络模型相比，我们发现 CS 图随着尺寸的增加而变得“更小”。
