Guiding "dot" towards desired edge placement - graphviz

Question

I have the following Graphviz code.
digraph {
North -> West
North -> East
North -> South
West-> South
East -> South
}
When using dot on this input file, it renders the graph with the direct edge between the North and South nodes on the outside:
My question: how can I get dot to render the North-to-South edge in between the East and West nodes?
Note that the graph above is a much simplified version of the problem I am encountering in the graph I actually want to improve, shown below (the thick red edge is the one I'd like dot to route via the more obvious way).

Answer 1

Pretty gross, but this works.
Uses a 3x3 matrix of nodes (visible & invisible).
Aligns via rank=same (https://graphviz.org/docs/attrs/rank/) & the group (https://graphviz.org/docs/attrs/group/) attribute. There is probably a "better" way to do this, but ...
digraph {
splines=false
North -> West
North -> East
North -> South
West-> South
East -> South
node[shape=plain style=invis label=""]
edge[style=invis]
{rank=same West -> central -> East }
{rank=same l1 -> North -> r1 }
{rank=same l2 -> South -> r2 }
{ node [group=V] North-> central-> South}
{ node [group=L] l1 -> West-> l2}
{ node [group=R] r1 -> East -> r2}
}
Giving:

Answer 2

If you need a specific edge to dominate your layout, you can use the weight = <integer> (where integer is a small positive value of about 10) attribute to make it as direct as possible. Conversely, negative values allow the layout engine to use more circuitous routes for unimportant edges. Edges with different weights are prioritised, but the layout is difficult to predict and can unexpectedly become ugly.
Avoid placing these additional constraints unnecessarily as the layout becomes increasingly brittle and small changes to the source can completely change the output.