Topological properties of integer networks

Tao Zhou, Bing-Hong Wang, P.M. Hui and K.P. Chan

Physica A: Statistical Mechanics and its Applications, 2006, vol. 367, issue C, 613-618

Abstract: Inspired by Pythagoras's belief that numbers represent the reality, we study the topological properties of networks of composite numbers, in which the vertices represent the numbers and two vertices are connected if and only if there exists a divisibility relation between them. The network has a fairly large clustering coefficient C≈0.34, which is insensitive to the size of the network. The average distance between two nodes is shown to have an upper bound that is independent of the size of the network, in contrast to the behavior in small-world and ultra-small-world networks. The out-degree distribution is shown to follow a power-law behavior of the form k-2. In addition, these networks possess hierarchical structure as C(k)∼k-1 in accord with the observations of many real-life networks.

Keywords: Complex networks; Integer networks; Upper bound of average distance (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:367:y:2006:i:c:p:613-618

DOI: 10.1016/j.physa.2005.11.011

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