Matrix Analysis of Hexagonal Model and Its Applications in Global Mean-First-Passage Time of Random Walks
Recent advances in graph-structured learning have demonstrated promising results on the graph classification task. However, making them scalable on huge graphs with millions of nodes and edges remains challenging due to their high temporal complexity. In this paper, by the decomposition theorem of L...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10029338/ |
| _version_ | 1811172245486174208 |
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| author | Xiaodong Yu Shahid Zaman Asad Ullah Ghulamullah Saeedi Xiujun Zhang |
| author_facet | Xiaodong Yu Shahid Zaman Asad Ullah Ghulamullah Saeedi Xiujun Zhang |
| author_sort | Xiaodong Yu |
| collection | DOAJ |
| description | Recent advances in graph-structured learning have demonstrated promising results on the graph classification task. However, making them scalable on huge graphs with millions of nodes and edges remains challenging due to their high temporal complexity. In this paper, by the decomposition theorem of Laplacian polynomial and characteristic polynomial we established an explicit closed-form formula of the global mean-first-passage time (GMFPT) for hexagonal model. Our method is based on the concept of GMFPT, which represents the expected values when the walk begins at the vertex. GMFPT is a crucial metric for estimating transport speed for random walks on complex networks. Through extensive matrix analysis, we show that, obtaining GMFPT via spectrums provides an easy calculation in terms of large networks. |
| first_indexed | 2024-04-10T17:26:40Z |
| format | Article |
| id | doaj.art-15d6291357a4481f9a47c4e5bef7851e |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-10T17:26:40Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-15d6291357a4481f9a47c4e5bef7851e2023-02-04T00:00:16ZengIEEEIEEE Access2169-35362023-01-0111100451005210.1109/ACCESS.2023.324046810029338Matrix Analysis of Hexagonal Model and Its Applications in Global Mean-First-Passage Time of Random WalksXiaodong Yu0Shahid Zaman1https://orcid.org/0000-0001-6152-8202Asad Ullah2https://orcid.org/0000-0003-1815-8538Ghulamullah Saeedi3https://orcid.org/0000-0003-2618-8980Xiujun Zhang4https://orcid.org/0000-0002-6704-031XSchool of Computer Science, Chengdu University, Chengdu, ChinaDepartment of Mathematics, University of Sialkot, Sialkot, PakistanDepartment of Mathematical Sciences, Karakoram International University Gilgit, Gilgit, PakistanDepartment of Mathematics, Polytechnical University of Kabul, Kabul, AfghanistanSchool of Computer Science, Chengdu University, Chengdu, ChinaRecent advances in graph-structured learning have demonstrated promising results on the graph classification task. However, making them scalable on huge graphs with millions of nodes and edges remains challenging due to their high temporal complexity. In this paper, by the decomposition theorem of Laplacian polynomial and characteristic polynomial we established an explicit closed-form formula of the global mean-first-passage time (GMFPT) for hexagonal model. Our method is based on the concept of GMFPT, which represents the expected values when the walk begins at the vertex. GMFPT is a crucial metric for estimating transport speed for random walks on complex networks. Through extensive matrix analysis, we show that, obtaining GMFPT via spectrums provides an easy calculation in terms of large networks.https://ieeexplore.ieee.org/document/10029338/Hexagonal modelLaplacian polynomialdecomposition theoremGMFPT |
| spellingShingle | Xiaodong Yu Shahid Zaman Asad Ullah Ghulamullah Saeedi Xiujun Zhang Matrix Analysis of Hexagonal Model and Its Applications in Global Mean-First-Passage Time of Random Walks IEEE Access Hexagonal model Laplacian polynomial decomposition theorem GMFPT |
| title | Matrix Analysis of Hexagonal Model and Its Applications in Global Mean-First-Passage Time of Random Walks |
| title_full | Matrix Analysis of Hexagonal Model and Its Applications in Global Mean-First-Passage Time of Random Walks |
| title_fullStr | Matrix Analysis of Hexagonal Model and Its Applications in Global Mean-First-Passage Time of Random Walks |
| title_full_unstemmed | Matrix Analysis of Hexagonal Model and Its Applications in Global Mean-First-Passage Time of Random Walks |
| title_short | Matrix Analysis of Hexagonal Model and Its Applications in Global Mean-First-Passage Time of Random Walks |
| title_sort | matrix analysis of hexagonal model and its applications in global mean first passage time of random walks |
| topic | Hexagonal model Laplacian polynomial decomposition theorem GMFPT |
| url | https://ieeexplore.ieee.org/document/10029338/ |
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