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Plot graph by distance from a given vertex

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.

But I've racked my head and lambda functions and whatnot to get this to work, and every graph plotting option and use of distance seems to go awry. I need help. I bet someone else does a lot more graph visualization than I do and will have an easy answer. (I suppose as a last resort I could use a dictionary for the locations and concoct info for that, but I am hoping it will be something I can do without having to construct the graph first.)