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Add support for the magnetic laplacian
The magnetic laplacian provides an alternative to symmetrizing the adjacency matrix for directed graphs. See e.g. "Graph Signal Processing for Directed Graphs based on the Hermitian Laplacian".
Could you maybe point us to a reference paper?
The magnetic Laplacian is widely mentioned, my fav is https://ecmlpkdd2019.org/downloads/paper/499.pdf. Note for q=0, the magnetic Laplacian is the same as the symmetrised one, so you could just introduce q as a kwarg and default it to 0 to be backwards compatible.
Btw, I'm not sure if it is intentional or not, but the directed symmetrised laplacian as it is currently in the code isnt using dw from the symmetrised W but self.dw.
I've put together a nice demo here: https://github.com/pulquero/sgw/blob/main/examples/graphwave.py
Thanks a lot.
I need to have a look at what you did, but I am really overworked. I will try to do it asap.
Came across another useful hermitian Laplacian for directed graphs: https://core.ac.uk/download/pdf/206608976.pdf (Laplacians and the Cheeger inequality for directed graphs, Fan Chung).