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A study of complex network using hyperbolic triangle group

Complex network representing many real-world systems in nature and society have some common structural properties such as power-law degree distribution, small average path length and strong clustering coefficient. Recent research has hinted that networks that have an underlying hyperbolic geometry a...

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Main Authors: Taha, M. H. M., Zainuddin, Hishamuddin, Mohd Shah, Nurisya, Chan, Kar Tim
Format: Conference or Workshop Item
Language:English
Published: 2016
Online Access:http://psasir.upm.edu.my/id/eprint/53694/1/A%20study%20of%20complex%20network%20using%20hyperbolic%20.pdf
http://psasir.upm.edu.my/id/eprint/53694/
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spelling my.upm.eprints.536942018-11-12T07:11:12Z http://psasir.upm.edu.my/id/eprint/53694/ A study of complex network using hyperbolic triangle group Taha, M. H. M. Zainuddin, Hishamuddin Mohd Shah, Nurisya Chan, Kar Tim Complex network representing many real-world systems in nature and society have some common structural properties such as power-law degree distribution, small average path length and strong clustering coefficient. Recent research has hinted that networks that have an underlying hyperbolic geometry are able to capture these properties. In this research, we focused on constructing the complex networks using abstract mathematical structures constructed by tessellating the hyperbolic triangle group on the hyperbolic plane. We report here how we can use Mathematica to generate corresponding tessellation from the group generators using linear fractional transformations. We then develop a programme to extract and visualize the network hidden in the tessellation for several hyperbolic triangle groups. 2016 Conference or Workshop Item PeerReviewed text en http://psasir.upm.edu.my/id/eprint/53694/1/A%20study%20of%20complex%20network%20using%20hyperbolic%20.pdf Taha, M. H. M. and Zainuddin, Hishamuddin and Mohd Shah, Nurisya and Chan, Kar Tim (2016) A study of complex network using hyperbolic triangle group. In: Fundamental Science Congress 2016, 9-10 Aug. 2016, Faculty of Science, Universiti Putra Malaysia. .
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description Complex network representing many real-world systems in nature and society have some common structural properties such as power-law degree distribution, small average path length and strong clustering coefficient. Recent research has hinted that networks that have an underlying hyperbolic geometry are able to capture these properties. In this research, we focused on constructing the complex networks using abstract mathematical structures constructed by tessellating the hyperbolic triangle group on the hyperbolic plane. We report here how we can use Mathematica to generate corresponding tessellation from the group generators using linear fractional transformations. We then develop a programme to extract and visualize the network hidden in the tessellation for several hyperbolic triangle groups.
format Conference or Workshop Item
author Taha, M. H. M.
Zainuddin, Hishamuddin
Mohd Shah, Nurisya
Chan, Kar Tim
spellingShingle Taha, M. H. M.
Zainuddin, Hishamuddin
Mohd Shah, Nurisya
Chan, Kar Tim
A study of complex network using hyperbolic triangle group
author_facet Taha, M. H. M.
Zainuddin, Hishamuddin
Mohd Shah, Nurisya
Chan, Kar Tim
author_sort Taha, M. H. M.
title A study of complex network using hyperbolic triangle group
title_short A study of complex network using hyperbolic triangle group
title_full A study of complex network using hyperbolic triangle group
title_fullStr A study of complex network using hyperbolic triangle group
title_full_unstemmed A study of complex network using hyperbolic triangle group
title_sort study of complex network using hyperbolic triangle group
publishDate 2016
url http://psasir.upm.edu.my/id/eprint/53694/1/A%20study%20of%20complex%20network%20using%20hyperbolic%20.pdf
http://psasir.upm.edu.my/id/eprint/53694/
_version_ 1643835462063751168
score 13.211869

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