I believe the only thing “missing” is the -n option on the neato command line. Like so: neato -n -Tpng myfile.gv>myfile.png (see FAQ | Graphviz)
neato will use the (new) node positions & generate appropriate (pretty much) edges.
Explicitly generating new edges is more of a challenge (see Fun with edges!)
Also note that neato is OK with (oblivious to) overlapping nodes, and the results can be fun (or not). (see Stupid Dot tricks)
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