# Is graph embedding linear in its maintaining of graph geometry?

It is claimed that the main goal of graph embedding methods is to pack every node's properties into a vector with a smaller dimension, so node similarity in the original complex irregular spaces can be easily quantified in the embedded vector spaces using standard metrics.

However, I can find no formal explanation as to why nodes with similar properties should be embedded so that their separation in embedded space respects their similarity. Is there such a proof, or is it a convenient consequence of embedding?