Four degrees of separation

November 30, 2011  |  Statistics

Facebook four degrees of separation

Testing the idea of six degrees of separation, first proposed by Frigyes Karinthy, the Facebook Data Team and researchers at the Università degli Studi di Milano found that most of us are connected by even fewer degrees, and average separation is getting smaller:

While we will never know if it was true in 1929, the scale and international reach of Facebook allows us to finally perform this study on a global scale. Using state-of-the-art algorithms developed at the Laboratory for Web Algorithmics of the Università degli Studi di Milano, we were able to approximate the number of hops between all pairs of individuals on Facebook. We found that six degrees actually overstates the number of links between typical pairs of users: While 99.6% of all pairs of users are connected by paths with 5 degrees (6 hops), 92% are connected by only four degrees (5 hops). And as Facebook has grown over the years, representing an ever larger fraction of the global population, it has become steadily more connected. The average distance in 2008 was 5.28 hops, while now it is 4.74.

So when you see random strangers, shake their hands and say hello. You're practically best friends.

Too bad there isn't an interactive we can enter random names on to see how close we are.

[Facebook]

10 Comments

  • I’ve seen this analysis pop up on a few sites and was wondering if the study is biased at all against the difficult nodes that tend to stretch the analysis. Anyone with a Facebook account has self selected themselves to be connected, so if you account for the resistant few (I know some), would that change the % significantly?

  • @Paul – it is bound to be biased in all sorts of ways. Facebook users are not a representative sample of all people and a ‘friend’ on facebook can be all sorts of things to all sorts of people depending on context & how they manage privacy etc. More recent users may well be more ‘promiscuous’ in acquiring ‘friends’. Hardly surprising then that ‘we’ appear to all be more closely connected. Having lots of data does not mean we can assume the results are ‘true’!

  • It is a fascinating study but I don’t like the way it is portrayed as changing the original 6 degrees study results. They seem to be studying different things, only superficially similar. 6 degrees is when you are asked and get to choose the next contact. 4 degrees is when you shotgun blast 730 million people on a social network with fairly loose relationships (I don’t “know” everyone on my Facebook friend list.)

  • LinkedIn has the interactive ability to enter a name and see how close you are — I think it is pretty cool. If you have a critical number of friends from diverse places, it is somewhat rare to find someone who is more than 3 hops away from you.

  • This is biased in the same way (only worse) that the original 6 degree study was biased. They both only measure based on those individuals who participate – neglecting those who do not. The 6 degree study only analyzed those letters that arrived and did not include that large number of letters that got lost or stuck in the middle of the process. Any social network study is focused only on those people in the social network, while ignoring those that are not members. None of these studies reflect the connectivity of society at large, let alone the whole human race. They only reflect the connectivity of highly connected individuals.

    Moreover, social network based studies seem to give unwarranted weight to “connection hoarders” whose superficial connectivity has little to do with useful or active connections. That can actually be corrected for and some studies attempt to correct for that (like using reciprocal connection counts)

  • Probably an interesting study, but wouldn’t those figures be way more clear (and easier to compare) if they plotted cumulative distribution functions instead?

  • Although I am sure there are issues with their analysis that us users on the outside would not understand or agree with, this is a very interesting finding. It is suggesting that computers have assisted in connecting us closer. Since the size of an egocentric community grows exponentially as a function of distance, systems like Facebook have implicitly introduced us to exponentially more people than without.

    As this number shrinks… things are going to get very interesting. I don’t know how, but I see a lot of good, and a lot of conspiracy theories could stem from it.

  • Andy Holaday November 30, 2011 at 4:08 pm

    Indeed, one conclusion that could be drawn is Facebook “promiscuity” has increased over time. The 4-5 hop buckets accounted for about 60% of pairs (15+45) in Jan 2008, up to about 95% (35+60) in May 2011. It doesn’t seem likely that so many people became that much more closely connected in 3 1/2 years, unless “connected” is defined fairly loosely.

  • log(7,000,000 population)/log(Dunbar’s number) = 4.5

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