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Authority, Influence in Social Networks [tentative thoughts]

I spent the day fiddling around with twitter and buzz, to see what signals I have at my disposal.

Eventually I’d like to get some metrics that quantify a few different aspects of human relationships:

  • Global influence (how much influence does this user have upon the world). This is pretty straightforward.
  • Local influence (how much influence does the user have within his more personal social sphere). This is less straightforward and much more interesting. Relatedly, who are the top influencers for an individual or for a clique of people. And can we get an InfluenceRank(a, b) between any two people, or a person and a group, etc.
  • Level of friendship, or closeness (how vague is that, huh?)
  • sub-graphs within a user’s FOAFs & FOAFOAFs that correspond to different social circles/publics/social identities. I’m pretty sure this is a well-studied problem, but it’s interesting to run the numbers for myself.

I’m just getting started, so here’s a working braindump…

I’d like to come up with some more rigorous definitions for these metrics (maybe look in some social psychology journals? read up on social networks?). And there are plenty of other stuff I want to measure, too…

Note: some of these are definition unidirectional (influence). Are any relationships or relationship-metrics bidirectional? (is friendship itself?)

Now, the signals that I have access to:

  • num followers
  • num followers in FOAF network
  • num followers in FOAFOAF network
  • num_replies(a, b)
  • num_reshares(a, b) (not in buzz, though…)
  • num_likes(a, b)
  • more?

These signals should also be normalized over how much a person communicates or follows in general — all we have is the observation “a is following b” or “a is talking to b”, we don’t know the internal impedence in a’s mind — do they follow lots of people, or is the fact that they are following this one person a more significant event?

I should probably also look at reciprocity. min(replies(a, b), replies(b, a)) for 2 users a and b will be very useful. Add on a minimum threshold (say, 3), and there’s a good proxy for friendship.

Another problem is that many of these metrics are so sparse! Just because A is friends with B doesn’t mean that A is going to necessarily comment/like/reshare that often.

I should probably also eliminate the “celebrities” of the network (people with friends/followers above a certain amount. Or at least treat them differently. These users are closer to proxies for measuring ideology or worldview of their followers, rather than “friends” in the canonical sense.

The hardest (most interesting?) part of all this will be evaluation. Once I have a metric, how can I quantify how good it is, beyond just eyeballing it? I have no labeled data…

This afternoon, I had some decent success approximating local influence as

num_followers_in_foaf_network – 0.01*num_followers_globally

(varying that 0.01 constant was a means of penalizing the global popularity of a person… keeping it at 0.01 got me the tech people who influence me personally, 0.05-0.1 got me my non-computery real-life-friends).

This one also worked nicely:

num_followers_in_foaf_network / (1 + log(num_followers_globally)

p.s. Many thanks to the authors of python-twitter and buzz-python-client, you made my life a lot easier…

One Comment

  1. This is intriguing. A couple thoughts:

    Are any relationships or relationship-metrics bidirectional? (is friendship itself?)

    I’d argue “yes”, but the arrows can be weighted differently (and usually are, I expect).

    num_followers_in_foaf_network / (1 + log(num_followers_globally)

    This, intuitively, seems better — but I’d love to see a histogram of the Twitter population’s number of followers/follows. I wonder how normal the distribution is. I would expect “not at all”: a bunch of peaks, out-of-scale at the very bottom, and I would not be surprised to see a dearth of users with number of followers between, say, 50k and 500k.

    I should probably also eliminate the “celebrities” of the network

    Maybe, but that’d be pretty hard. And also misleading for the celebs who use their big account as their personal account. It’s maybe along the lines of “I hope I don’t become famous. It’d be a pain to change all my avatars on sites that don’t allow one to use pictures of famous people.” It seems by this consideration that celebs couldn’t have real friends — or, at the very least, information about friendship would be discarded by your model. It’s a small population, but “celebrities are people too”. ;-)

    Add on a minimum reply threshold (say, 3), and there’s a good proxy for friendship.

    Ah, I see you are unacquainted with the concept of “flame war”. Welcome to the Internet, it’s a fine place. ;-)

    Posted on 29-Jan-11 at 22:06 | Permalink

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