Difference between Symmetrically normalized Laplacian matrix versus graph laplacian matrix

Question

I am trying to understand the graph laplacian matrix in Graph Convolution networks.

To get a basic understanding of graph laplacian matrix I am referring to this

https://mbernste.github.io/posts/laplacian_matrix/

However, the two definitions are different. What is the difference? are they the same? What does symmetric normalization mean here?

$L \neq D - A$

The graphs we are dealing with here are taxi demand at different regions of a city at different points in time.

Thanks.

Answer 1

The above one is called normalized graph Laplacian, while the below is (unnormalized) graph Laplacian. As you can remark, $D^{1/2} \tilde{L} D^{1/2}= L$, where $\tilde{L}$ is the normalized Laplacian and $L$ is the unnormalized one.