I have some graphs I'd like to be able to plot in such a way that I can set a "top" vertex $v$, and then make all vertices distance 1 from $v$ be maybe 1 cm/in lower down, the ones distance 2 away be twice and far, and so forth. As it happens, each such set of vertices have no edges between them, so this will look just like a Hasse diagram/lattice/whatever and be meaningful.