Graph Representation Learning: Question about eigenvector of Laplacian

[Master1022]

TL;DR

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 $L$:
$$L = D - A$$
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.

 

[JFerreira]

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.