Set node direction on graphviz

Suppose this code using neato:

graph sample {
  layout=neato
  overlap=false
  splines=true
  tailclip=false
  headclip=false
  A -- I
  A -- J
  A -- B
  A -- H
  A -- E
  A -- K
  B -- D
  B -- C
  B -- L
  C -- M
  C -- N
  C -- O
  D -- P
  D -- Q
  E -- R
  F -- A
  G -- F
  H -- J
}

This gives us this diagram:

What I need is to place a node X, always fixed in a position south from his parent node. i.e. If I put another relation A -- X, X should be always placed south from A. And I don't really care where everything else ends up.

I've looked into the pos attribute, but it doesn't seems to be the solution since X is not really in a fixed position, but on a position relative to his relation.

Also tailport and headport, but they only define from where the edge will come out/in, but don't really affect the direction of the node.

Update

An additional image to make things clearer:

I don't require neato, but I don't want the graph to look like a UD or LR dot tree, I don't want it to be linearly ordered. circo, fdp, sfdp, twopi are alright too.

The neato program supports multiple modes, one of which can probably give you what you want. In particular, if you set mode=ipsep, you can specify dot-like constraints that are honored during the layout. For example, I take your graph and use the graph attributes

mode=ipsep
diredgeconstraints=true
levelsgap=0.5

The first turns on ipsep mode, the second tells the model to support directed edges as in dot, and the last specifies how strong the separation should be. I then set the edge dir attribute to none

edge[dir=none]

and add an edge A -- X [dir=1]

The dir=1 indicates this edge should induce a directional constraint. If I then run neato, I get the appended picture.

The Graphviz attribute documentation http://www.graphviz.org/content/attrs provides more information about these attributes.