From dense adjacency matrix to edge_index

[AndreaPi]

I have the following dense adjacency matrix:

adjacency_matrix = torch.tensor([[0., 1., 1., 1.],
                                 [1., 0., 1., 1.],
                                 [1., 1., 0., 1.],
                                 [1., 1., 1., 0.]])

This corresponds to a 4-nodes graph, where each node is connected each other node but not to itself.

Usually I see that conversion from this matrix to edge_index is done this way:

edge_index = (adjacency_matrix > 0).nonzero().t()

Why do we need (adjacency_matrix > 0)? Wouldn't we get exactly the same result with adjacency_matrix.nonzero().t()? This is the case for all examples I tried so far.

[Padarn]

I think these are equivalent unless your adjacency_matrix contains edge weights too

[rusty1s]

That is correct. Transferring the adjacency matrix to a mask first will result in unnecessary computation and memory overheads though.

[AndreaPi]

Hi @rusty1s,

with

Transferring the adjacency matrix to a mask first

you mean this operation (adjacency_matrix > 0), right?

[rusty1s]

Yes, this will create a bool matrix of shape [num_nodes, num_nodes].