Laplacian Eigenvectors of Graphs - 2019 Fall ~ 2020 Spring
Book
Laplacian Eigenvectors of Graphs: Perron-Frobenius and Faber-Krahn Type Theorems by Türker Biyikoglu, Josef Leydold, Peter F. Stadler
[You may find a pdf version of the book in NSYSU library, or other institutes that have subscribe Springer.]
Participants
Jephian Lin, Chih-Wei Chen, Akeny Li, Yi-Hua Li, Daniel Radil, Ting-Ying Li, An-Rong Wu; all others are welcome.
General guidelines
It is better to be slow and clear than fast but vague---if you need more time, we may postpone the next speaker.
Find corresponding proofs if not provided---see the references of the book.
It is okay to have something not understood---we put the keywords at the bottom of the page, and we will conquer it at the end.
Be prepared by the scheduled time, though the schedule might change.
Schedule
We follow the regular venue and time below; it there is any change, it will be annotated in the schedule.
Venue: SC4013
Time: Tuesday 9:10 ~ 10:00 (2020 Spring)
Venue: SC4009-0 (the room next to the library on the 4th floor); Time: Thursday, 16:10 ~ 17:00 (2019 Fall)
12/13, Friday, 9:10 ~ 10:00; Introduction [~1.3; Jephian]
12/20, Friday, 9:10 ~ 10:00; Related matrices [~1.4; Jephian]
12/26, Thursday; Generalized Laplacian [~1.8; Jephian]
1/2, Thursday; Discrete Calculus [~2.7; Akeny]
1/9, Thursday; Perron--Frobenius Theorem [~2.8; YH Li]
3/5, Thursday; Perron--Frobenius Theorem [~2.8; YH Li]
3/12, Thursday; Perron--Frobenius Theorem [~2.8; YH Li]
3/19, Courant's Nodal Domain Theorem [~3.2; Jephian]
3/26, Fiedler's vector [~3.4; TY Li]
4/9, Courant--Herrmann Conjecture [~3.6; Daniel]
4/16, Nodal Domain on trees and cographs [~4.2; 陳冠穎]
4/23, Nodal Domain on other graphs [~4.3; AR Wu]
4/30, Hyperplane arrangement and Hillclimbing algorithm [~5.2; 魏齊]
5/7, Numerical experiments [~5.4; 郭明憲]
5/14, Faber--Krahn type inequalities [~7.9; 黃進璋]
5/21, Unweighted trees and semiregular trees [~6.4; 黃齡誼]
5/28, Rearrangements [~6.5; 黃元亨]
6/4, Perturbations and branches [~end; 陳伯誠]
6/2, Drawing Graphs by Eigenvectors: Theory and Practice [吳牧修]
6/9, On the Kemeny constant and stationary distribution vector for a Markov chain [鄭力豪]
6/9, Kemeny's constant and an analogue of Braess' paradox for trees [Trang Lê Thị]
6/11, Normalized Cuts and Image Segmentation [丁俊恩]
Keywords to be explored later
Elementary landscape (p. 4)
cut (p. 13)
Related papers
R. Merris. Laplacian matrices of graphs: A survey. Lin. Algebra Appl., 197–198:143–176, 1994.
M. Belkin and P. Niyogi. Laplacian eigenmaps and spectral techniques for embedding and clustering. In Advances in Neural Information Processing Systems 14 (NIPS 2001), pages 585–591, Cambridge, 2002. MIT Press.
T. Pisanski and J. Shawe-Taylor. Characterising graph drawing with eigenvectors. J. Chem. Inf. Comput. Sci., 40:567–571, 2000.