Characterizing several properties of high-dimensional random Apollonian networks. (16th December 2020)

• Record Type: Journal Article
• Authors: Zhang, Panpan
• Editors: Masuda, Naoki
• Is Part Of: Journal of complex networks. Volume 8:Number 4(2020)
• Publication Date: 2020-12-16
• Subjects: degree profile -- distance -- high-dimensional random Apollonian networks -- small world -- sparsity -- topological index; Numerical analysis -- Periodicals; Computer networks -- Periodicals; Social networks -- Periodicals; 518.05
• DOI: 10.1093/comnet/cnaa038
• Languages: English
• ISSNs: 2051-1310

Abstract

Abstract: In this article, we investigate several properties of high-dimensional random Apollonian networks, including two types of degree profiles, the small-world effect (clustering property), sparsity and three distance-based metrics. The characterizations of the degree profiles are based on several rigorous mathematical and probabilistic methods, such as a two-dimensional mathematical induction, analytic combinatorics and Pólya urns, etc. The small-world property is uncovered by a well-developed measure—local clustering coefficient and the sparsity is assessed by a proposed Gini index. Finally, we look into three distance-based properties; they are total depth, diameter and Wiener index.