Avoiding cycles in a directed graph

I'm using the following table to represent an acyclic directed graph:
   CREATE TABLE edge(       id SERIAL PRIMARY KEY,       child INTEGER NOT NULL,       parent INTEGER,       UNIQUE
(child,parent)   );
 

I see there is an example in the online docs for detecting cycles in
recursive queries, and I've adapted the example query to the table above:
   WITH RECURSIVE search_graph(parent, child, id, depth, path, cycle)   AS (           SELECT e.parent, e.child, e.id,
1,            ARRAY[e.id],             false           FROM edge e         UNION ALL           SELECT e.parent,
e.child,e.id, sg.depth + 1,             path || e.id,             e.id = ANY(path)           FROM edge e, search_graph
sg          WHERE e.parent = sg.child AND NOT cycle   )   SELECT * FROM search_graph;
 

That's great to avoid looping forever on queries, but what about
preventing anyone from inserting edges that would create cycles in the
first place?  I reckon I'll need a trigger of some sort, but nothing
I've tried has enabled me to do the cycle check as part of the trigger
to avoid inserting an edge that would create a cycle.  I tried having
the non-recursive SELECT use NEW.parent, NEW.child, etc. but that isn't
working.  Is there any way to do this, or do I have to just insert the
edge, check if it cycles, and delete it if it does?

Thanks.
-Tony