What ready available algorithms could I use to data mine twitter to find out the degrees of separation between 2 people on twitter.
How does it change when the social graph keeps changing and updating constantly.
And then, is there any dump of twitter social graph data which I could use rather than making so many API calls to start over.
There was a company offering a dump of the social graph, but it was taken down and no longer available. As you already realized - it is kind of hard, as it is changing all the time.
I would recommend checking out their social_graph api methods as they give the most info with the least API calls.