A Twitter Analog to PageRank

A few weeks ago, there was a flame war about Twitter authority, and I was all too eager to throw fuel on the pyre. But now that the blogosphere has calmed down a bit, I’d like to propose a ranking measure that I think might work. My apologies if it isn’t original. In fact, if you’ve seen it elsewhere, please point me to it.

Let me start with the assumptions about the model:

• Influence(X) = Expected number of people who will read a tweet that X tweets, including all retweets of that tweet. For simplicity, we assume that, if a person reads the same message twice (because of retweets), both readings count.
• If X is a member of Followers(Y), then there is a 1/||Following(X)|| probability that X will read a tweet posted by Y, where Following(X) is the set of people that X follows.
• If X reads a tweet from Y, there’s a constant probability p that X will retweet it.

This model is obviously simplistic in all three assumptions. But I think it’s a reasonable first cut. In particular, it accounts for the inflation that occurs from people who follow in the hopes of reciprocity. There’s less value in being followed by someone who follows a lot of people, because that person is less likely to read your messages or retweet them.

Of course, there’s room for adding more realism to this model, but I hope it is at least close enough to the truth to be interesting.

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From this model, it’s easy to measure someone’s influence recursively, assuming that we know the constant retweet probability p:

The recursion is infinite over a graph with directed cycles, but rapidly converges as high powers of p approach zero. I would think this measure wouldn’t be hard to compute to a reasonable accuracy.

This measure strikes me as a PageRank for Twitter or any system with similar properties. There’s more room for nuance, but I at least find this approach more plausible than the ones I’ve seen. It also strikes me as hard to game, since it isn’t counting retweets, and it’s hard to add much influence through followers who don’t have any influence themselves.

What do folks think? Has anyone tried this? If not, is there anyone who’d like to try hacking an application to compute it? Either way, please let me know!