Although I've worked with CNN's for over a year, I am struggling to understand how GCN's work. I've read several papers, and I find myself out of my depth when they talk about Chebyshev polynomials or Fourier spaces.

The descriptions talk about using an adjacency matrix as input, and perhaps my primary confusion is how I can supply such a matrix to a convolutional neural network (if that is what is in fact what is done). I can't just convolve over the matrix as if it were an image because spatial similarity in the matrix (i.e. rows/cols that are near to each other) doesn't signify actual closeness between nodes in the graph.

Can anyone clarify this?