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...
| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/53694/ http://psasir.upm.edu.my/id/eprint/53694/1/A%20study%20of%20complex%20network%20using%20hyperbolic%20.pdf |
| _version_ | 1848852351364890624 |
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| author | Taha, M. H. M. Zainuddin, Hishamuddin Mohd Shah, Nurisya Chan, Kar Tim |
| author_facet | Taha, M. H. M. Zainuddin, Hishamuddin Mohd Shah, Nurisya Chan, Kar Tim |
| author_sort | Taha, M. H. M. |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T10:36:42Z |
| format | Conference or Workshop Item |
| id | upm-53694 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:36:42Z |
| publishDate | 2016 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-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. . |
| spellingShingle | Taha, M. H. M. Zainuddin, Hishamuddin Mohd Shah, Nurisya Chan, Kar Tim A study of complex network using hyperbolic triangle group |
| title | 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_short | A study of complex network using hyperbolic triangle group |
| title_sort | study of complex network using hyperbolic triangle group |
| url | http://psasir.upm.edu.my/id/eprint/53694/ http://psasir.upm.edu.my/id/eprint/53694/1/A%20study%20of%20complex%20network%20using%20hyperbolic%20.pdf |