I've learned it from a [book about database concepts](https://www.mitp.de/IT-WEB/Datenbanken/Datenbanken-Konzepte-und-Sprachen-oxid.html) (chapter 11.5.2):
> Traversing order
>
> The SQL standard provides an optional traversing clause, which determines the order in which the the nodes of the graph are visited. This is possible via the clause
>
> `SEARCH BREADTH FIRST BY column SET pseudo-column`
>
> the width search is possible, through which first all directly connected nodes (in
> in our example the places that can be reached directly from the starting point)
> then the nodes are output over two edges (places marked with
> (which can be reached with a single change), then the nodes over three edges
> etc.
>
> On the other hand, by specifying the clause
>
> `SEARCH DEPTH FIRST BY column SET pseudo-column`
>
> forced a depth search. At first a path is searched until the end
> before the next path is visited.
>
> In both cases, column specifies the attribute to be used for navigation -
> so it must be an attribute from the condition of the recursive compound
> be. The clause generates a pseudo column in the query result,
> in the non-recursive part of the request by an ORDER BY clause
> can be evaluated.
>
> (Translated with www.DeepL.com/Translator (free version))
So, to me it looked as if it were part of SQL standard. Appearently, it's supported in Oracle and IBM DB2. The latter contains the following [example](https://www.ibm.com/support/knowledgecenter/ssw_ibm_i_73/sqlp/rbafyrecursivequeries.htm):
```sql
WITH destinations (departure, arrival, connections, cost) AS
(SELECT f.departure, f.arrival, 0, price
FROM flights f
WHERE f.departure = 'Chicago'
UNION ALL
SELECT r.departure, b.arrival, r.connections + 1,
r.cost + b.price
FROM destinations r, flights b
WHERE r.arrival = b.departure)
SEARCH BREADTH FIRST BY arrival SET ordcol
SELECT *
FROM destinations
ORDER BY ordcol```