Congrats, you found the Google Drive API version 3 several hours before we officially announced it. :)
In v3, there is no longer a parents collection. Instead, you get the parents property by doing a files.get with the child's ID. Ideally, you would use the fields parameter to restrict the response to just the parent(s). Note: A file may have more than one parent, so be prepared to handle multiple parents.
You can get a sense of the changes from v2 to v3 by looking at the migration cheat sheet.