I guess it looks nice but aside from that what else could I say about this graph? What sorts of statements about this could I make and try to prove? ...Later, I will try coloring based on the g.c.f. of each pair, i.e. if it were 2 I would use blue, if it were 3 red, etc.
Lastly... if this already exists somewhere and has been studied already, where could I read further about it?