TunkRank

March 12th, 2009 by Carl | Filed under Algorithms, PageRank, Social Media, Twitter, mathematics.

Twitter is becoming an increasingly popular social media tool. An interesting post on Science for SEO to do with Twitter. Wouldn’t it be great to find out who was an influential member of the Twitter community? Google has an effective algorithm developed by its founders Larry Page and Sergie Brin, known as PageRank. A similar algorithm has been created for the Twitter network, by Daniel Tunkelang called, you guessed it, TunkRank.
tunkrank1

TunkRank measures your influence in the Twitter world. For those that are familiar with PageRank it uses a similar concept of traversing the directed graph the graph of  follower and those following.

How does it work?

It is a recursive relationship which converges to the answer when applied to the graph of links between members of Twitter. There is no good way to describe it in word so you will have to take the mathematics.

Influence(X) = sum{Y in Followers(X)} {}{{1+ p * Influence(Y)}/{delim{vert}{Following(Y)}{vert} }}

There is an assumption in the constant p, the probability of a message being retweeted. This is a fudge-factor at the moment and may be more useful to make this a function of the number of tweets per day. Up to a point you are more likely to follow or retweet a link from someone that tweets regularly but not so often that it becomes annoying.

Each term in the sum depends on the influence and number of people following person Y. The more followers this person has, the less it will add to the total. The influence of person Y increase the value. This term is greatest when you are followed by an influential person that is followed by few people. Which seems fair enough.

This shares several features with the original PageRank algorithm, it is recursive on the network uses directed graph. If you have a large number of links from a page the influence from this page is  reduced. Similarly, a following a large number of people reduces your influence.

Let’s see how a few of the movers and shakers I follow fare:

TunkRank Scores:

Twitter Name Percentile Raw Score
BarackObahma 100 9270.040
StephenFry 100 3548.070
Shoemoney 100 277.462
Randfish 100 77.241
Problogger 100 463.470
Graywolf 100 58.826
Thegypsy 99 10.371
Misscj 96 6.051
DazzlinDonna 1 1
drnedflanders 86 3.001
hobo_web 1 1
fantomaster 1 1

Scores are given from 1-100, a larger score being more influential. A raw score is also given which allows you to compare individuals. For example, Stephen Fry has more than 1500 times more influence than me, which is what you would expect. There are some influential people in the table that have low scores of 1, they are influential people, I promise, but their graphs have not been crawled yet.

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