# Iterate over acyclic subdigraphs

I have a graph `D`

, and would like to iterate over its (maximal) acyclic subdigraphs (not necessarily induced).

My current best bet is to iterate over all permutations of the vertex set of D and, for each one, create an acyclic digraph A by going through each edge of D in turn and adding to A only those edges `ij`

where `i`

is less than `j`

in the current permutation.

But this seems awfully inefficient.

More precisely:

```
D = DiGraph()
D.add_edges([[0,1],[0,2],[1,2],[1,3],[2,3],[3,4],[4,5],[4,6],[5,6],[5,0],[6,0]])
n = D.num_verts()
for p in Permutations(n):
A = DiGraph()
for e in D.edges():
if p[e[0]] < p[e[1]]:
A.add_edge(p[e[0]] -1,p[e[1]] -1)
# Here A is a maximal acyclic subdigraph of D
do_stuff(A)
```

Any ideas would be greatly appreciated.