I actually did read through that discussion but the solution is not what I'm looking for. Using the `path` and `instr` method you showed there will cut off paths that become cycles but it won't cut off paths that revisit nodes.
Take for example the directed-acyclic graph:
```
1
|\
2 3
|/
4
|\
5 6
|/
7
```
```
$ cat bfs_test.sql
create table edges(fromNode integer, toNode integer);
insert into edges(fromNode, toNode) values
(1, 2),
(1, 3),
(2, 4),
(3, 4),
(4, 5),
(4, 6),
(5, 7),
(6, 7);
with recursive
bfs_tree(id, visited, distance) as (
select 1, '/' || 1 || '/', 0
union all
select toNode, visited || toNode || '/', distance + 1
from edges, bfs_tree
where fromNode = id and instr(visited, '/' || toNode || '/') == 0
order by 3 asc
)
select * from bfs_tree;
$ sqlite3 < bfs_test.sql
1|/1/|0
2|/1/2/|1
3|/1/3/|1
4|/1/2/4/|2
4|/1/3/4/|2
5|/1/2/4/5/|3
6|/1/2/4/6/|3
5|/1/3/4/5/|3
6|/1/3/4/6/|3
7|/1/2/4/5/7/|4
7|/1/2/4/6/7/|4
7|/1/3/4/5/7/|4
7|/1/3/4/6/7/|4
```