# Isn't graph embedding a step back from non-euclidean space?

As I understand, we use graph embedding to make a euclidean representation of non-euclidean structure - graph. Does it mean that conceptually we just take a step back to, may be, more complex, but still grid processing?

• Can you be more specific? My feeling is that you're mixing up discrete/graph/grid with (non) euclidean-ness. Nodes of a graph may not even have positions, so theyre neither euclidean nor non-euclidean. Unless you're thinking of a case where they do. – bogovicj Jul 8 '20 at 0:01
• @bogovicj I'm beginner here, may be I do really mix up something. My question was about loosing data and loosing the advantages of graph structures. As I understand, we use graphs to hold relations and properties more then position and coordinates. I mean this by non-euclidean-ness. Correct me if I am wrong, an idea of embedding is to map graph structure to linear coordinate system (like plane, or volume, or higher-dimensional linear space). So, this way we just transform an initial data to more simple and space-like format. Doesn't it mean that we loose initial graph advantages? – Nikita Jul 9 '20 at 9:00
• Thanks, that helps. I'll try to write an answer on those points, and we can continue the conversation after if I'm not clear enough / am still missing the point. – bogovicj Jul 9 '20 at 14:45