Six degrees of Twitter

Its hard to be original. When I first signed up with Twitter, I liked it straight away, somewhat to my surprise, as I have never liked Facebook, and saw Twitter and Facebook as the twin spearheads of trivia. One pleasant Twitter surprise was the spare simplicity. Only does one thing. No ads. Strict 140 character limit. That kind of discipline can be good for artistic expression. An idea jumped into my head. Twitter Haikus ! Ten minutes later I realised that Twitter is swarming with haikus. Those of you on Twitter can just search on #haiku; others can see a constant stream of twitter haikus here and more nice stuff here .

Half an hour later I thought … how about a Twitter Novel … twenty first century Dickens ? However … I guess I don’t need to carry on.  For your enjoyment here is the stream from the currently ongoing Twitter version of Romeo and Juliet.

A week later I had noticed that when I got a new folllower, it was kinda fun clicking at random on their followers or followees, to see where I ended up. Pretty soon I found myself having “small world” thoughts – how many links separate any two Twitterers ? Could be a game, or a research project, thought I.

Scooped again. Through TechCrunch, to which I am mildly addicted, I learned of a report by a company called Sysomos which apparently gives us the answer. They analysed 5.2 billion connections and concluded that Twitter users are on average separated by 4.67 steps.

However, I couldn’t figure out what they really did. They say they analysed Twitter “friendships” but Twitter doesn’t have “friends”. It has followers and followees. They can’t be using followees, as any fule can search for a famous person and follow them. Bingo. One step. But they obviously don’t mean followers either, because the article refers to the phenomenon of coming across one of your followers after a few friendship links. This article suggests that a reasonable definition of “friend” on Twitter is someone you have directed a post to (with “@”) at least twice. But who knows if thats what Sysomos did ?

I have just sweated through two stressful peer review experiences. But getting cross with the Sysomos report reminded me how good the peer reviewed literature is. You couldn’t get away with not defining your methods at MNRAS.

Is this six-degrees-small-world just pop nonsense or is there really something to it ? Yes, a graph with six links can connect extremely large numbers of nodes. But that doesn’t tell us much about how real world networks actually develop. Don’t networks divide into islands ? There is a good wikipedia page on the subject and at least one quite famous serious paper ( Watts and Strogatz 1998) but this web article casts doubt on the whole thing.

I’d tell you the answer If only I had any energy left after solving quasars, marking exams, and reading nine million grant proposals.


18 Responses to Six degrees of Twitter

  1. “Is this six-degrees-small-world just pop nonsense or is there really something to it ?”

    A) What’s the deal with the space before the question mark?

    B) Yes, there is something to it. It is similar to the Erdös number. Six degrees of separation, six degrees of Kevin Bacon (I assume you were aware of that reference), Pegg numbers in folk-rock etc.

  2. andyxl says:

    Phillip : (A) Simple illiteracy I guess. (B) Of course one can always define an Erdos or Bacon number for any individual. The point is that popular mythology says that any individual can be linked to any other individual with six steps. This is a striking statement which I think is not proven.

    I hadn’t heard of Pegg numbers ! There is a separate hypothesis that there are key influential individuals in any field who are linked to more people than others. I think this is in Gladwell’s book, which I haven’t read.

    • “The point is that popular mythology says that any individual can be linked to any other individual with six steps. This is a striking statement which I think is not proven.”

      I don’t see how one could prove it, mathematically, for all people. However, I think I can link myself to any well known person in less than 6 steps. If an arbitrary person can do so as well, then at most we are separated by the sum. (There is nothing special about well known people, other than the facts taht a) they provide an obvious “target” and b) they usually have more links.

      I doubt the originator of the Pegg number (Dave Pegg (bassist with Fairport Convention) has a Pegg Number of 0, those who played on the same album or tour a Pegg number of 1 etc) had heard of the Erdös number, but the concept is the same.

  3. Mark Evans says:

    Thanks for talking about the report. The way that we determined a “friendship” was by counting the total number of @ connections within the Twitter network. Perhaps connections may be have a better word but what we were trying to do was provide people an idea of how connected everyone is.

    cheers, Mark

    Mark Evans
    Director of Communications
    Sysomos Inc.

  4. andyxl says:

    Thank you for chipping in ! Hope I wasn’t too rude. Is there a REAL version of the report somewhere ?

  5. andyxl says:

    Phillip – I challenge you to demonstrate your link to the President of Malawi.

    • One of the first people I met when I moved to Germany in 1983 was Loki Schmidt, wife of former German Chancellor Helmut Schmidt. That probably makes it obvious. 🙂 (The father in the family I lived in as an exchange student had an old friend who, after years as a sea captain, founded an environmental conservation organisation, protecting sea birds in the North Sea etc. Loki is a member of this organisation.) I don’t have all the names, but Helmut Schmidt knew many heads of state personally, maybe not that of Malawi, but certainly someone who knew the president of Malawi, who certainly has a link to the current president. Q.E.D. 🙂

    • Telescoper’s blog is all abuzz with Erdos numbers and Phillip referenced this page, so I thought I’d add another route to the President of Malawi in under 6 steps that would work for lots of us. It would go like this: Malawi is in the Commonwealth, so if you can get a link to the Queen in under 5 steps, you’ve done it. If you can find a link to a current or past Astronomer Royal in four steps, you’re there. We haven’t yet even used the RAS, Royal Society, foreign international facilities, press/media contacts, etc… It’s so simple it’s prosaic, really…

      • Malcolm Currie says:

        Or know somebody with a gong.

        I once shared an office in Herstmonceux Castle with Sir Richard Woolley after he had retired. 🙂

    • James Kay says:

      An old story told at Edinburgh University concerned a group of students arguing about the number of degrees of separation. One of them picked up a newspaper, noted the headline was about Hastings Banda, and asked “How would you find a chain which links me to him?”

      An ancient ‘permanent student’ was sitting nearby, but had not been part of the discussion. He now spoke up: “I used to share digs with him” !

  6. Steve Warren says:

    I once gave a lift to a member of the Malawi Congress Party who received a monthly allowance from Hastings Banda the President of Malawi at the time, who you might agree is only one link from the current president.

  7. Steve Warren says:

    I should add that Philip worked with Dan Marlow on gravitational lenses, and I examined Dan Marlow’s thesis. So that’s Philip, Dan, myself, someone whose name I have forgotten, Hastings Banda, the current president.

    Names in Malawi are themselves a topic of great fascination. Many are plucked from a dictionary. Examples include Gold, Limestone, Greedy. One of the best is Elastic Banda.

    • On names:

      “Though the title looks like a play on “Made in USA,” it’s also the teen heroine’s name (quite common in Peru), pronounced “Mah-day-ah-noosa.” Portrayed with subtlety by newcomer Magaly Solier, Madeinusa is the favorite of her father Cayo (Ubaldo Huaman), the town mayor, who’s disturbing sexual advances toward his daughter, are coupled with the jealousy of Madeinusa’s sister Chale (Yiliana Chong). Ever since their mother fled to Lima, a sourness has descended over the household, symbolized by the presence of dead rats.”

      I won’t mention Nosmo King. Or should I?

      Not to mention Ima Hogg (yes, real).

  8. andyxl says:

    Crikey that was good. Hmm. Anybody else got a challenge for Phillip or Steve ?

  9. Four degree, five degree, six degree, rock!

    Anyone with an interest in English rock music from the 1960s and 1970s should check out Pete Frame’s wonderful ROCK FAMILY TREES books. Based on having read these more than 20 years ago, I hereby claim that any musician from a reasonably well known English rock band of the 1960s or 1970s is connected to any other similarly defined musician by fewer than 6 degrees of separation, even if one defines a connection as strictly as having recorded an album together (other criteria, such as having toured together, appeared on the same bill, sex with the same groupies etc are much less strict).

    Challenges? Surely you can make them more difficult than the link between me and the president of Malawi?!

  10. Martin E. says:

    Martin Harwit has been looking into networks of astronomers. One source he uses is:
    M. E. J. Newman, PNAS 101, 5200, (2004); PNAS, 98, 404 (2001)
    Most of us are in a single highly connected group with a few strong nodes of highly influential individuals. Unfortunately, he didn’t identify the individuals, so we can’t cluck cluck over how awful it is that A is so powerful, while we are not.
    Harwit should have a book on it out soon.

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