Rate limit is insanely restricting for friends/ids and followers/ids


I’m writing an application that involves graphing a users Twitter network to a given depth.
In my immediate network (which I’m using for testing), I have 18 friends and 2 followers, giving a pool of 20.

My application (given my id) fetches my friends and followers by these API methods, sends the ids to lookup, which returns the user objects nicely.
However, I want to expand the depth of the network graph, so I can see friends of friends (or at least, see the interconnections between my immediate friends).

This is rendered impossible as far as I can tell, but the extremely restricting rate limit for API methods friends/ids and followers/ids.
15 per/app? That’s insane! I can’t even complete my tiny network, and that’s not even considering cursored results for popular people.

Is there any other method I should be using to see the interconnections among my immediate network?
If not, why are these limits so tiny?!

(friendships/lookup is equally useless with a rate limit of 15)