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Clustering and the hyperbolic geometry of complex networks
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Candellero, Elisabetta and Fountoulakis, Nikolaos (2016) Clustering and the hyperbolic geometry of complex networks. Internet Mathematics, 12 (1). doi:10.1080/15427951.2015.1067848 ISSN 1542-7951.
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Official URL: http://dx.doi.org/10.1080/15427951.2015.1067848
Abstract
Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social networks. In this paper, we consider what is called the global clustering coefficient of random graphs on the hyperbolic plane. This model of random graphs was proposed recently by Krioukov et al. [Krioukov et al.] as a mathematical model of complex networks, under the fundamental assumption that hyperbolic geometry underlies the structure of these networks. We give a rigorous analysis of clustering and characterize the global clustering coefficient in terms of the parameters of the model. We show how the global clustering coefficient can be tuned by these parameters and we give an explicit formula for this function.
Item Type: | Journal Article | ||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||
Library of Congress Subject Headings (LCSH): | Geometry, Geometry, Hyperbolic, Biomathematics, Computational complexity, System theory -- Mathematical models, Computer algorithms | ||||||||||
Journal or Publication Title: | Internet Mathematics | ||||||||||
Publisher: | Taylor & Francis | ||||||||||
ISSN: | 1542-7951 | ||||||||||
Official Date: | 3 March 2016 | ||||||||||
Dates: |
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Volume: | 12 | ||||||||||
Number: | 1 | ||||||||||
DOI: | 10.1080/15427951.2015.1067848 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||
Date of first compliant deposit: | 29 May 2016 | ||||||||||
Date of first compliant Open Access: | 28 July 2016 |
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