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Add support for the magnetic laplacian #99

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pulquero opened this issue Jun 27, 2021 · 6 comments
Open

Add support for the magnetic laplacian #99

pulquero opened this issue Jun 27, 2021 · 6 comments

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@pulquero
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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".

@nperraud
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Could you maybe point us to a reference paper?

@pulquero
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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.

@pulquero
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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.

@pulquero
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I've put together a nice demo here: https://github.com/pulquero/sgw/blob/main/examples/graphwave.py

@nperraud
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nperraud commented Jun 29, 2021 via email

@pulquero
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pulquero commented Oct 1, 2021

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).

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