Postgres - Convert adjacency list to nested JSON object

Using WITH RECURSIVE (https://www.postgresql.org/docs/current/static/queries-with.html) and JSON Functions (https://www.postgresql.org/docs/current/static/functions-json.html) I build this solution:

db<>fiddle

The core functionality:

    WITH RECURSIVE tree(node_id, ancestor, child, path, json) AS  (
      SELECT 
          t1.node_id, 
          NULL::int, 
          t2.node_id,
          '{children}'::text[] || 
             (row_number() OVER (PARTITION BY t1.node_id ORDER BY t2.node_id) - 1)::text,-- C
          jsonb_build_object('name', t2.name, 'children', array_to_json(ARRAY[]::int[])) -- B
      FROM test t1
      LEFT JOIN test t2 ON t1.node_id = t2.parent_node                                   -- A
      WHERE t1.parent_node IS NULL

      UNION

      SELECT
          t1.node_id, 
          t1.parent_node, 
          t2.node_id,
          tree.path || '{children}' || (row_number() OVER (PARTITION BY t1.node_id ORDER BY t2.node_id) - 1)::text, 
          jsonb_build_object('name', t2.name, 'children', array_to_json(ARRAY[]::int[]))
      FROM test t1
      LEFT JOIN test t2 ON t1.node_id = t2.parent_node
      INNER JOIN tree ON (t1.node_id = tree.child)
      WHERE t1.parent_node = tree.node_id                                                -- D
    )
    SELECT                                                                               -- E
        child as node_id, path, json 
    FROM tree 
    WHERE child IS NOT NULL ORDER BY path

Every WITH RECURSIVE contains a start SELECT and a recursion part (the second SELECT) combined by a UNION.

A: Joining the table agains itself for finding the children of a node_id.

B: Building the json object for the child which can be inserted into its parent

C: Building the path where the child object has to be inserted (from root). The window function row_number() (https://www.postgresql.org/docs/current/static/tutorial-window.html) generates the index of the child within the children array of the parent.

D: The recursion part works as the initial part with one difference: It's not searching for the root element but for the element which has the parent node of the last recursion.

E: Executing the recursion and filtering all elements without any children gives this result:

node_id   path                      json
2         children,0                {"name": "node2", "children": []}
4         children,0,children,0     {"name": "node4", "children": []}
5         children,0,children,1     {"name": "node5", "children": []}
6         children,0,children,2     {"name": "node6", "children": []}
3         children,1                {"name": "node3", "children": []}
7         children,1,children,0     {"name": "node7", "children": []}
8         children,1,children,1     {"name": "node8", "children": []}

Though I found no way to add all children elements in the recursion (the origin json is no global variable; so it always knows the changes of the direct ancestors, not their siblings), I had to iterate the rows in a seconds step.

That's why I build the function. In there I can do the iteration for a global variable. With the function jsonb_insert I am inserting all calculated elements into a root json object - using the calculated path.

CREATE OR REPLACE FUNCTION json_tree() RETURNS jsonb AS $$
DECLARE
    _json_output jsonb;
    _temprow record;
BEGIN
    SELECT 
        jsonb_build_object('name', name, 'children', array_to_json(ARRAY[]::int[])) 
    INTO _json_output 
    FROM test 
    WHERE parent_node IS NULL;

    FOR _temprow IN
        /* Query above */
    LOOP
        SELECT jsonb_insert(_json_output, _temprow.path, _temprow.json) INTO _json_output;
    END LOOP;

    RETURN _json_output;
END;
$$ LANGUAGE plpgsql;

Last step is calling the function and make the JSON more readable (jsonb_pretty())

{
    "name": "node1",
    "children": [{
        "name": "node2",
        "children": [{
            "name": "node4",
            "children": []
        },
        {
            "name": "node5",
            "children": []
        },
        {
            "name": "node6",
            "children": []
        }]
    },
    {
        "name": "node3",
        "children": [{
            "name": "node7",
            "children": []
        },
        {
            "name": "node8",
            "children": []
        }]
    }]
}

I am sure it is possible to optimize the query but for a sketch it works.