Prevent and/or detect cycles in postgres

To answer my own question, I came up with a trigger that prevents this:

CREATE OR REPLACE FUNCTION detect_cycle() RETURNS TRIGGER AS
$func$
DECLARE
  loops INTEGER;
BEGIN
   EXECUTE 'WITH RECURSIVE search_graph(id, parentid, name, depth, path, cycle) AS (
        SELECT g.id, g.parentid, g.name, 1,
          ARRAY[g.id],
          false
        FROM node g
      UNION ALL
        SELECT g.id, g.parentid, g.name, sg.depth + 1,
          path || g.id,
          g.id = ANY(path)
        FROM node g, search_graph sg
        WHERE g.id = sg.parentid AND NOT cycle
)
SELECT count(*) FROM search_graph where cycle = TRUE' INTO loops;
IF loops > 0 THEN
  RAISE EXCEPTION 'Loop detected!';
ELSE
  RETURN NEW;
END IF;
END
$func$ LANGUAGE plpgsql;

CREATE TRIGGER detect_cycle_after_update
AFTER UPDATE ON node
FOR EACH ROW EXECUTE PROCEDURE detect_cycle();

So, if you try to create a loop, like in the question:

UPDATE node SET parentid = 2 WHERE id = 1;

You get an EXCEPTION:

ERROR:  Loop detected!

Your trigger simplified and optimized, should be considerably faster:

CREATE OR REPLACE FUNCTION detect_cycle()
  RETURNS TRIGGER
  LANGUAGE plpgsql AS
$func$
BEGIN
   IF EXISTS (
      WITH RECURSIVE search_graph(parentid, path, cycle) AS ( -- relevant columns
          -- check ahead, makes 1 step less
         SELECT g.parentid, ARRAY[g.id, g.parentid], (g.id = g.parentid)
         FROM   node g
         WHERE  g.id = NEW.id  -- only test starting from new row
         
         UNION ALL
         SELECT g.parentid, sg.path || g.parentid, g.parentid = ANY(sg.path)
         FROM   search_graph sg
         JOIN   node g ON g.id = sg.parentid
         WHERE  NOT sg.cycle
         )
      SELECT FROM search_graph
      WHERE  cycle
      LIMIT  1  -- stop evaluation at first find
      )
   THEN
      RAISE EXCEPTION 'Loop detected!';
   ELSE
     RETURN NEW;
   END IF;
END
$func$;

You don't need dynamic SQL, you don't need to count, you don't need all the columns and you don't need to test the whole table for every single row.

CREATE TRIGGER detect_cycle_after_update
AFTER INSERT OR UPDATE ON node
FOR EACH ROW EXECUTE PROCEDURE detect_cycle();

An INSERT like this has to be prohibited, too:

INSERT INTO node (id, name,parentid) VALUES (8,'D',9), (9,'E',8);