PostgreSQL get all possible origin/destination node sequence

Question

I have this PostgreSQL table with node of a directed graph:

node_id | node_sequence 
-----------------------
   1           1
   2           2 
   3           3 

I'd return a table with all the possible origin destination sequence (only in one direction) between the node: (1,2); (1,2,3); (2,3). So the output table should be:

node_id
 ----
   1
   2
   1
   2
   3
   2
   3

Maybe WITH RECURSIVE is the right thing to do but I cannot understand how.

Answer 1

Edit from initial answer:
You seem to have 2 constraints you do not mention in your question:

• You want sequences of at least 2 elements
• Elements in a sequence must be in ascending order and consecutive

Here is a simple query that does it (CTE GraphNode should be replaced with your table):

WITH RECURSIVE GraphPath AS (
SELECT G2.Node, ARRAY[G1.Node, G2.Node] AS GraphPath /* Start with 2 elements */
FROM GraphNode G1
JOIN GraphNode G2 ON G1.Node + 1 = G2.Node
UNION ALL
SELECT N.Node, P.GraphPath || N.Node
FROM GraphNode N
JOIN GraphPath P ON N.Node = 1 + P.Node 
), GraphNode AS (
SELECT UNNEST(ARRAY[1,2,3]) AS Node
)
SELECT GraphPath
FROM GraphPath
ORDER BY GraphPath