More precisely, if v i (i = 1, 2) is the node such that e i ∈ in(v i ), then D[e 1 ↔ e 2 ] has e 1 ∈ in(v 2 ) and e 2 ∈ in(v 1 ) but is otherwise identical to D. It is not difficult to see that the edge interchange operator we have just defined might introduce cycles, that is, D[e 1 ↔ e 2 ] may no longer be a DAG.
in what follows we will use this operator in a restricted way, such that the resulting graph is still a DAG.