# Graph Representation Learning: Question about eigenvector of Laplacian

• I
Master1022
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##:
$$L = D - A$$
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?