The "height" of a vertex in a rooted tree is the length of the longest downward path to a leaf from that vertex. The "height" of the tree is the height of the root. The "depth" of a vertex is the length of the path to its root ("root path"). This is commonly needed in the manipulation of the various self-balancing trees, AVL trees in particular. The root has depth zero, leaves have height zero, and a tree with only a single vertex (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (a tree with no vertices, if such are allowed) has depth and height −1.