Degree Matrix in Spectral Clustering

Question

I am currently learning spectral clustering.

We decomposite the Laplacian Matrix which calculated by L = D - W.

W is the adjacent matrix.

However, I have found a lot codes online like spectral clustering

they directly calculate D by diag(sum(W)).

I know that D should be degree matrix which means each value on the diagonal are the degree for each point.

But if W is a weighted graph , diag(sum(W)) is not equal to the actual "Degree matrix"...

Why they still do this.

Answer 1

When you work with weighted graphs you can compute the degree matrix from the weighted adjacency matrix, some time it is good to have weights because they hide geometric information. Moreover, if you have the weighted adj matrix computing degree matrix using the binary form of your weighted adj matrix is easy. In addition, I think your question has more theoretical (e.g. Mathoverflow) than programming foundation (e.g stackoverflow) ;). In any case, you should consult this link for more intuitive explanation of L and its geometric relation.

Good luck :)