In a Parent-Child circular relationship, how to show parent only relattionship

Thanks for the tips Hakan! That's the lightbulb that I can needed.
Here's my
MATCH (i:Inc)
MATCH (i)-[r:HAS_CHILD *1..3]-(i2)
WHERE count { (i2)--() } = 2
MATCH(i2)-[rd:HAS_CHILD]->()
DELETE rd

Now all the leaf does have any relationship to the parent.

Next step is to make this graph a DAG...i.e. I need to remove the circular relationship between any parent nodes. i.e. between 746431 and 746424, there should only be ONE relationship. So we need to remove ONE of the directed graph, doesn't matter which one.

I thought about following the same approach except the count condition > 2, but that won't work because it would impeded on all the r:HAS_CHILD on the leaf nodes.
Any suggestion?