Each vertex is placed at its unique top node. Vertices at a node of depth $d$ receive the ranks $(d - 1)(w + 1), …, d(w + 1) - 1$ in a fixed order, and $u$ is an ancestor of $v$ if it has smaller rank and its top node is an ancestor of that of $v$. The endpoints of an edge lie in a common bag, so their top nodes are both ancestors of that node, hence comparable.