Influence Rank
There is a company called TunkRank, whose mission is to rank the influence of various Twitter users. Using their services, you can find out the how influential a Twitter user is, and can also request that they refresh or re-calculate the influence of a user. Their service is based on an algorithm called TunkRank by Daniel Tunkelang. In this algorithm, a user’s influence is defined as the expected number of people who will read a tweet that he/she tweets, including all retweets of that tweet. As such, their model assumes that the influence of a Twitter user is based on the number of followers that he/she has, but not on the number of people he/she follows. In fact, they say that a user’s “usefulness” as a follower is lesser the more people that they follow. This follows from the simple reasoning that the more people a user follows, the less “attention” that they can give to each person, and so the less likely they are to read each of the tweets from all of the people that they follow.
One can see that this is a direct analogue of the PageRank algorithm (with similarities to the the hubs and authorities algorithm), applied to a social network, specifically Twitter. We can think of the users as the “web pages” in this ranking algorithm, and think of following someone as “linking” to them. And just as in PageRank, your influence “flows out” to every node that you are linked to, and you “collect” influence from users that link to you. You divide your attention among everyone that you follow, and you will be more influential by being followed by lots of followers, especially followers who don’t follow very many people, since you will have a large base of followers who will give you lots of attention. This is analagous to being linked to by many reliable web pages, which is an indication that you yourself are a reliable web page, thus increasing your ranking.
Sources:
http://thenoisychannel.com/2009/01/13/a-twitter-analog-to-pagerank/