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Clustering and the Hyperbolic Geometry of Complex Networks

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Algorithms and Models for the Web Graph (WAW 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8882))

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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. [22] as a mathematical model of complex networks, implementing the assumption that hyperbolic geometry underlies the structure of these networks. We do 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, giving an explicit formula.

Nikolaos Fountoulakis: This research has been supported by a Marie Curie Career Integration Grant PCIG09-GA2011-293619.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Warwick Coventry, Coventry, CV4 7AL, UK

    Elisabetta Candellero

  2. School of Mathematics, University of Birmingham, Edgbaston, B15 2TT, UK

    Nikolaos Fountoulakis

Authors
  1. Elisabetta Candellero
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  2. Nikolaos Fountoulakis
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Corresponding author

Correspondence to Nikolaos Fountoulakis .

Editor information

Editors and Affiliations

  1. Ryerson University, Toronto, Ontario, Canada

    Anthony Bonato

  2. University of California San Diego, La Jolla, California, USA

    Fan Chung Graham

  3. Ryerson University, Toronto, Ontario, Canada

    Paweł Prałat

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Candellero, E., Fountoulakis, N. (2014). Clustering and the Hyperbolic Geometry of Complex Networks. In: Bonato, A., Graham, F., Prałat, P. (eds) Algorithms and Models for the Web Graph. WAW 2014. Lecture Notes in Computer Science(), vol 8882. Springer, Cham. https://doi.org/10.1007/978-3-319-13123-8_1

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  • DOI: https://doi.org/10.1007/978-3-319-13123-8_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13122-1

  • Online ISBN: 978-3-319-13123-8

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