There is a large number of sites like Twitaholic or Twittergrader that offer rankings of Twitter users depending on the number of followers, influence, etc. I haven't found much information, though, on how do they compute these rankings.
My guess is that they begin with a handful users and keep exploring the followers' graph, while periodically updating the information of the users they already know of.
So the question is: is this the right approach or is there a more trivial way of doing it?
The sites you mention started years ago, and at that time they were given whitelisting by Twitter, which means that they can make tens of thousands of API requests per hour. Twitter no longer gives out new whitelisted accounts, so this type of analysis cannot be done by new sites. New accounts are only allowed to make 350 API requests per hour.