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The emergence of the giant component in random graphs on the hyperbolic plane

Banff International Research Station for Mathematical Innovation and Discovery

We consider a recent model of random geometric graphs on the hyperbolic plane developed by Krioukov et al. (Phys. Rev. E 2010). This may be also viewed as a geometric version of the well- known Chung-Lu model of inhomogeneous random graphs and turns out to have basic properties that are ubiquitous in complex networks. We consider the size of the largest component of this random graph and show that a giant component emerges when the basic parameters of the model cross certain values. We also show that the fraction of vertices that are contained there converges in probability to a certain constant, which is related to a continuum percolation model on the upper-half plane. This is joint work with Tobias Müller and Michel Bode.

Mathematics; Combinatorics; Probability theory and stochastic processes

video/mp4

Author affiliation: University of Birmingham

2017-05-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61567

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/