Two cumulative distributions for scale-freeness of dynamic networks

Xiaomin Wang and Bing Yao

Physica A: Statistical Mechanics and its Applications, 2020, vol. 556, issue C

Abstract: It is well-known that the scale-free networks are ubiquitous in nature and society and have been one of the hotspot topic in complex networks. Recently, scholars presented a large quantity of scale-free networks by calculating cumulative distribution. The purpose of this paper is to discuss the relationship between two cumulative distributions, namely, cumulative distribution, edge-cumulative distribution. Here, firstly, we introduce a relationship between degree distribution and cumulative distribution. Secondly, we introduce the definition of cumulative distribution and edge-cumulative distribution, and compare the relationship between them. Thirdly, we apply algorithmic techniques to construct three deterministic networks, calculate their cumulative distribution and edge-cumulative distribution, and analyze the relationship between cumulative distribution and edge-cumulative distribution. Finally, we offer some open problems for future research in order to understand the interplay between the degree distribution, cumulative distribution and edge-cumulative distribution.

Keywords: Recursive graph model; Sierpinski network model; Apollonian network model; Power-law distribution; Cumulative distribution (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:556:y:2020:i:c:s0378437120303733

DOI: 10.1016/j.physa.2020.124747

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