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Clustering and the Hyperbolic Geometry of Complex Networks

  • Elisabetta Candellero
  • Nikolaos Fountoulakis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8882)

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.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of Warwick CoventryCoventryUK
  2. 2.School of MathematicsUniversity of BirminghamEdgbastonUK

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