Yes, the Graph API is horribly documented. I don't see any documentation for an "application" type, but they do reference an application's info in the docs:
https://graph.facebook.com/2439131959
So, perhaps you can get the application's members using the Group syntax?
https://graph.facebook.com/2439131959/members
You'll need an authenticated session to test it. Otherwise, it looks like Facebook is pushing us to use FQL to send queries directly:
http://developers.facebook.com/docs/reference/fql/application
You can execute FQL queries by
fetching
https://api.facebook.com/method/fql.query?query=QUERY.
You can specify a response format as
either XML or JSON with the format
query parameter.
So you can pass a FQL query to get information about your application.