Lack of Gromov-hyperbolicity in small-world networks

Yilun Shang

Open Mathematics (2012)

  • Volume: 10, Issue: 3, page 1152-1158
  • ISSN: 2391-5455

Abstract

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The geometry of complex networks is closely related with their structure and function. In this paper, we investigate the Gromov-hyperbolicity of the Newman-Watts model of small-world networks. It is known that asymptotic Erdős-Rényi random graphs are not hyperbolic. We show that the Newman-Watts ones built on top of them by adding lattice-induced clustering are not hyperbolic as the network size goes to infinity. Numerical simulations are provided to illustrate the effects of various parameters on hyperbolicity in this model.

How to cite

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Yilun Shang. "Lack of Gromov-hyperbolicity in small-world networks." Open Mathematics 10.3 (2012): 1152-1158. <http://eudml.org/doc/269148>.

@article{YilunShang2012,
abstract = {The geometry of complex networks is closely related with their structure and function. In this paper, we investigate the Gromov-hyperbolicity of the Newman-Watts model of small-world networks. It is known that asymptotic Erdős-Rényi random graphs are not hyperbolic. We show that the Newman-Watts ones built on top of them by adding lattice-induced clustering are not hyperbolic as the network size goes to infinity. Numerical simulations are provided to illustrate the effects of various parameters on hyperbolicity in this model.},
author = {Yilun Shang},
journal = {Open Mathematics},
keywords = {Graph hyperbolicity; Small world; Complex networks; graph hyperbolicity; small world; complex networks},
language = {eng},
number = {3},
pages = {1152-1158},
title = {Lack of Gromov-hyperbolicity in small-world networks},
url = {http://eudml.org/doc/269148},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Yilun Shang
TI - Lack of Gromov-hyperbolicity in small-world networks
JO - Open Mathematics
PY - 2012
VL - 10
IS - 3
SP - 1152
EP - 1158
AB - The geometry of complex networks is closely related with their structure and function. In this paper, we investigate the Gromov-hyperbolicity of the Newman-Watts model of small-world networks. It is known that asymptotic Erdős-Rényi random graphs are not hyperbolic. We show that the Newman-Watts ones built on top of them by adding lattice-induced clustering are not hyperbolic as the network size goes to infinity. Numerical simulations are provided to illustrate the effects of various parameters on hyperbolicity in this model.
LA - eng
KW - Graph hyperbolicity; Small world; Complex networks; graph hyperbolicity; small world; complex networks
UR - http://eudml.org/doc/269148
ER -

References

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