(I didn't see any question like this on the CSTheory exchange -- apologies if it has already been answered.)
In a nested hierarchy, a higher level includes all levels below it.
The classic example of a "non-nested" hierarchy is military rank. A general is not a lieutenant, so military rank is a non-nested hierarchy.
But here's my objection -- doesn't a general have all the skills a lieutenant has, plus more skills? So in that sense, isn't every general a lieutenant? He may not be called "lieutenant", but in reality he is a lieutenant-plus.
Thus, I am wondering... can we really say that any hierarchy is non-nested?