I've been reading different papers regarding graph convolution and it seems that they come into two flavors: spatial and spectral. From what I can see the main difference between the two approaches is that for spatial you're directly multiplying the adjacency matrix with the signal where for the spectral version you're using the Laplacian matrix. Am I missing something or are there any other differences that I am not aware of?
After I read multiple explanations from different sources I think I found the main difference between the two methods. Implementation wise the only difference is the matrix that you're multiplying the signal with (Laplacian/adjacency matrix). But by using the Laplacian, you're encoding the graph structure (in-out degree of each node) which dictates how a signal should "diffuse" in the network.