Transitive, Directed Graph in SQL - mysql

Question

I am trying to make a graph transitive using SQL.
I do not see, why this should not work:
with recursive recursive_table(from, to) as (
SELECT * FROM Graph
UNION ALL
SELECT r1.to, r2.from FROM recursive_table r1, recursive_table r2
WHERE r1.from = r2.to
UNION ALL
SELECT * FROM recursive_table
)
SELECT * FROM recursive_table;
In every recursion, I take the elements specified in the not transitive Graph (1), everything which is the result of the next recursion (3) and everything which results out of the next recursion (2).
However, SQL says:
[2021-02-12 10:36:05] [HY000][3577] In recursive query block of Recursive Common Table Expression 'recursive_table', the recursive table must be referenced only once, and not in any subquery
A sample output would be the following:
Input:
+------+------+--+
| Col1 | Col2 | |
+------+------+--+
| 1 | 2 | |
| 2 | 3 | |
| 1 | 4 | |
| 4 | 5 | |
+------+------+--+
Output:
+------+------+--+
| Col1 | Col2 | |
+------+------+--+
| 1 | 2 | |
| 2 | 3 | |
| 1 | 4 | |
| 4 | 5 | |
| 1 | 3 | |
| 1 | 5 | |
+------+------+--+
So, mathematically speaking,
If you can go from a to b in a finite amount of steps > 0, add (a,b) to the graph.
For example, you can go from 1 to 2 and from 2 to 3 on the input data, therefore you can go from 1 to 3.
Another example is a circle with n - knots.
This means, the input would be something like this...
+------+------+--+
| Col1 | Col2 | |
+------+------+--+
| 1 | 2 | |
| 2 | 3 | |
| 3 | ... | |
| ... | n | |
| n | 1 | |
+------+------+--+
The correct output would be [n] X [n]

Answer 1

It is a little hard to say exactly why your code doesn't work. There are multiple potential issues:
from is not a valid column name.
Recursive CTEs rarely have two union alls.
Recursive CTEs do not usually reference the recursive CTE multiple times.
In any case, correct code is simpler:
with recursive recursive_table(col1, col2) as (
SELECT col1, col2
FROM graph
UNION ALL
SELECT r1.col1, g.col2
FROM recursive_table r1 JOIN
graph g
ON r1.col2 = g.col1
)
SELECT *
FROM recursive_table;
Here is a db<>fiddle.
Note that both this code and your code assume that the graph has no cycles. That is not part of your question, but if it is an issue, ask a new question.