A graph is planar if it can be drawn on a plane with no wires crossing. Some graphs are inherently nonplanar, like that puzzle about the three houses and three utility pipes. But it's possible to draw a planar graph with the nodes badly positioned so that there are unnecessary crossings.
Arguably planar graphs are easier to read, and for sure they're easier to draw on circuit boards, only one level needed.
I definitely knew that, and even that certain nonplanar graphs (like the one you mentioned) are planar on, say, a torus (topological definition); I just didn't happen to think of that when you used the word "planarness". Now if you'd said "planar graph"...
Yeah I make up words sometimes. "Planar graph" wouldn't have fit the context of the sentence. I guess I expect people who know "planar" and know "-ness" to work out what the compound means. I could have said "planarity" or "planarhood" instead!
I don't blame you; I do exactly the same thing. ("it'sn't")
Can you two possibly keep your off-off-off-topic chatter just down to just being off-topic please! 