A tree has a root, leaves, and what?

Question

The root of a tree is special, in that it has no parents. The leaves are special in that they have no children. The other nodes each have exactly one parent and more than zero children. Is there a word for that third kind? (Myself, I have been calling them "middle" or "tree-middle".)

Answer 1

Usually you just need the concept of "internal nodes", which are nodes that are not leaves, because usually there is no need to distinguish between the root node and other internal nodes. The reason is that the root is often an arbitrary choice, whereas the unrooted tree still has the same internal nodes.