Graph Representation Learning: Question about eigenvector of Laplacian

  • I
  • Thread starter Master1022
  • Start date
  • #1
Master1022
611
116
TL;DR Summary
What does the eigenvector of the laplacian matrix actually represent?
Hi,

I was reading the following book about applying deep learning to graph networks: link. In chapter 2 (page 22), they introduce the graph Laplacian matrix ##L##:
[tex] L = D - A [/tex]
where ##D## is the degree matrix (it is diagonal) and ##A## is the adjacency matrix.

Question:
What does an eigenvector of a Laplacian graph actually represent on an intuitive level?

Also, I apologize if this is the wrong forum - should I have posted elsewhere?

Thanks in advance.
 

Answers and Replies

  • #2
JFerreira
8
6
If you haven't found the answer to your question, please see this thread. It talks about the fact that the eigenvalues of the adjacency matrix describe closed walks on the graph, and much more.

You can find other results, searching, for instance, for "graph Laplacian matrix eigenvalues " on SearchOnMath.
 

Suggested for: Graph Representation Learning: Question about eigenvector of Laplacian

  • Last Post
Replies
9
Views
713
  • Last Post
Replies
0
Views
319
  • Last Post
Replies
2
Views
329
  • Last Post
Replies
2
Views
175
Replies
35
Views
1K
  • Last Post
Replies
12
Views
471
Replies
7
Views
2K
Replies
2
Views
549
  • Last Post
Replies
22
Views
928
Replies
17
Views
728
Top