Oh yes, unfortunately, you can't do this perfectly. There are some graphs that cannot be embedded in Euclidean space in any number of dimensions, e.g. a 4-cycle

Oh yes, unfortunately, you can't do this perfectly. There are some graphs that cannot be embedded in Euclidean space in any number of dimensions, e.g. a 4-cycle with distance measured by path length. It's a good-enough approximation for visualization purposes, though.