簡易檢索 / 詳目顯示
| 研究生： |
許家承 Jia-Cheng Syu |
|---|---|
| 論文名稱： |
拉普拉斯居中度研究概述 A Review of the Study on Laplacian Centrality |
| 指導教授： |
葉鴻國
Hong-Gwa Yeh |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 論文出版年： | 2021 |
| 畢業學年度： | 109 |
| 語文別： | 英文 |
| 論文頁數： | 28 |
| 中文關鍵詞： | 拉普拉斯居中度 、拉普拉斯矩陣 |
| 外文關鍵詞： | Laplacian Centrality, Laplacian matrix |
| 相關次數： | 點閱：5 下載：0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
拉普拉斯居中度是一個圖形參數，用來測量頂點 (node) 的相對重要性。在本文中，我們通過介紹文獻中有關拉普拉斯中心性的主要結果與其證明，來簡要介紹拉普拉斯居中度。我們還對一些原始較複雜的證明，提供了新的簡潔證明。
Laplacian centrality is a graph parameter to measure the importance of a vertex (comparing to other vertices in the same graph). In this paper we give a brief introduction of Laplacian centrality by presenting key results about Laplacian centrality in the literature together with proofs. We also provide simple and shorter new proofs (along the line of the original complicated proofs) for some these results.
[1] F. Chung, Spectral Graph Theory, American Mathematical Society, 1997.
[2] Felipe Grando, Lisandro Z. Granville, Luís C. Lamb, Machine Learning in Network Centrality Measures: Tutorial and Outlook, ACM Computing Surveys, Vol. 51, No. 5, Article 102 (2019) 102:1-102:32.
[3] M. Lazic, On the Laplacian Energy of a Graph, Czechoslovak Mathematical Journal, 56 (2006)
1207-1213.
[4] Xingqin Qi, Eddie Fuller, Qin Wu, Yezhou Wu, and Cun-Quan Zhang, Laplacian centrality: A new centrality measure for weighted networks Information Sciences 194 (2012) 240-253.
[5] Xingqin Qi, Robert D.Duval, Kyle Christensen, Edgar Fuller, Arian Spahiu, Qin Wu, Yezhou Wu, Wenliang Tang and Cunquan Zhang, Terrorist Networks, Network Energy and Node Removal: A New Measure of Centrality Based on Laplacian Energy, Social Networking, 2 (2013) 19-31.
[6] Hong-Gwa Yeh, Class Notes for Graph Theory, Fall 2020 and Spring 2021, National Central University, Taiwan.
