I don't see a whole bunch of use for it. However if the empty graph is a connected graph and every connected graph has a spanning tree then... It all depends what you want to do with it. I thought of generating functions. The [first article][1] in a Google search says "It will turn out to work better if we ... do not count the empty tree as a rooted tree." So that indicates that "who knows, it could have been better the other way but it isn't." It also seems to say "it is a tree but not a rooted one." Then again, the author does not need to take a position since rooted trees are what is needed. I guess one can always say "non-empty" trees if needed. [1]: http://math.berkeley.edu/~mhaiman/math172-spring10/trees.pdf