Question

I have a database table like following:

column 1 | column 2

x | Y

y | z

z | x

So basically x->y->z->x.

Now I have to detect such entries in the DB. One solution could be take these entries and make a graph in memory and then detect the cycle with a cycle finding algorithm. I would rather do it with an SQL query if possible though.

Answer 1

SQLite does not support recursive queries, so the best you can do is to detect cycles of fixed length using self-joins. You can’t detect cycles of arbitrary length.

Here’s an example of a join that finds cycles of length 2, like the example you showed in your question.

SELECT ...
FROM t AS t0
JOIN t AS t1 ON t0.column2 = t1.column1
JOIN t AS t2 ON t1.column2 = t2.column1
WHERE t2.column2 = t0.column1

---

Re your comment:

If you need to detect cycles of arbitrary length, all I can suggest is that you must store more than the direct links. You must also store the transitive closure, i.e. every path through your graphs. That’s the best way to make this search efficient. Of course it takes a lot more storage space to do that, but there’s your tradeoff. And it takes less extra space than you think.

I’ve done a transitive closure design for trees, but not acyclic graphs. See my answer to What is the most efficient/elegant way to parse a flat table into a tree? or my presentation Models for Hierarchical Data with SQL.