Tag Archives: Sebastiano Vigna

6 degrees of separation now 4.74 on Facebook [REVISED 4/12/12]


A 2011 examination by Facebook and the University of Milan of all 721 million Facebook users (over 10% of the world’s population) found that Facebook users were less than five degrees of separation from anyone else. “While 99.6 per cent of all pairs of users are connected by paths with five degrees (six hops), 92 per cent are connected by only four degrees (five hops)” and was even lower if the searcher and the target lived in the same country.  As more users get onto Facebook, the degrees of separation are dropping; the average was 5.28 three years ago and is 4.74 today.  See studies “The Anatomy of the Facebook Social Graph” and “Four Degrees of Separation“.  [Of course, as many users of Facebook know who get “friended” by people who are not their friends or whom they have never met, this 4.74 degrees of separation no doubt includes a lot of “friends” along with real ones and this pushes down this theoretical level of interconnectedness that the researchers found.]

This runs against the grain of other work that has cast doubt on the “6 degrees of separation” theory for the population as a whole.  NPR had an interesting discussion on Talk of the Nation (January 25, 2008) regarding whether it is true that we really are no more than 6 degrees of separation apart from anyone on the planet. They invited on Judith Kleinfeld and Steven Strogatz (a professor in network theory).

Background: “6 degrees of separation” got its conception from a study by Stanley Milgram in the 1950s testing how many links it took to connect a random mid-Westerner from Omaha or Wichita with a random person from Boston. The study seemed to show that subjects were on average 6 path links away from each other. [Each recipient of a letter was supposed to send to the target recipient if he/she knew the target directly, or forward on the person who the subject thought would be most likely to know the target; this procedure was iterated and the number of links were totaled.] The Milgram methodology has been criticized by some. This has been generalized into the claim that any two people in the world are 6 degrees separated, although Milgram never used the phrase ‘degrees of separation’ and he only showed that the median chain link was 5.5 not that all chain lengths were 6 or less.  Some links took as many as 12 links although it is possible that in reality there were much shorter links possible.] . The ‘6 degrees notion’ was recently tested in a Small World experiment by Duncan Watts at Columbia which has found an average path length of worldwide volunteers of five, although there are some problems with their methodology (since they only took volunteers who might have volunteered because they wanted to test whether they were as cosmopolitan and as well-connected as they believed).

Note: Albert-Laszlo Barabasi  in his interesting book Linked reveals that Milgram had a Hungarian father and a Romanian mother and notes that in 1929 a very famous Hungarian writer Frigyes Karinthy wrote a story entitled “Lancszemek” (or “Chains”) in which a member of a group proposed a test to show that the world’s people were closely connected: he bet that through at most five acquaintances any of the then 1.5 billion inhabitants of the earth could be linked.  While it is unclear whether Milgram ever read this story, his Hungarian lineage suggests that perhaps through his father he might have heard of this first known conjecture of “five degrees of separation.”

Kleinfeld, in trying to digitally recreat Milgram’s experiment, found problems with the experiment (detailed in the current issue of Discover magazine with the wonderful title “If Osama’s only 6 degrees of separation away, why can’t we find him?“) Among them were that Milgram only counted the path length of the letters that actually reached their recipients, not the majority of letters that never reached them.  (Kleinfeld notes that only 3 of 60 letters reached their target in Milgram’s original study and the following study had a completion rate of only 29%.) Strogatz admits that this was a problem that Milgram was aware of and observed  that it is challenging to figure out how to interpret the letters that didn’t make it to the final person since it could be that one of the intervening links simply didn’t forward on the letter rather than the fact that the path length would have been much longer if completed.  [Kleinfeld in the article suggests that the fact that Milgram recruited participants by buying mailing lists skewed the partiicpants to be more high-income.  Because most American friendships are same-class, it is easier sociologically much easier for high-income subjects to find high-income targets than if the experimenta; subject  had to locate a target of a different economic class.]

The low completion rates also mirror some results Duncan Watts got in his Small World experiment. Recruiting volunteers on the web globally to see how many links separated them, Watts et al. began 24,163 “degree of separation” experiments. Only 384 of these were completed (or about 1.5%), and those completed had an average path length of slightly over 4 links.  Watts surveyed respondents who dropped out of the experiment and fewer than one in 200 respondents indicated that they didn’t continue the chain because they didn’t know whom to send it to.  This tends to support the notion that the completed links may not be different than the uncompleted ones in total path length but in the interest of the intervening links to complete the experiment.

Strogatz notes that this research really raises 3 interesting questions. First, “given two people, is there a short path connecting them? That is a question of existence. Does a chain exist? The second question has to do with search. Can people find these short paths if they exist? And a third question is, … even if the paths did exist and people could find them, could they use them to exert any influence on a person at the distant end?” Strogatz notes that regardless of any imperfections in Milgram’s approach, short paths definitely do exist, and people if motivated can find these paths. But he said that the issue of one’s leverage at six degrees of separation is much more doubtful.

Strogatz also discussed evidence of this “small world” in other settings and some ideas of how this might be used.

As to the answer about finding Osama bin Laden, Watts indicates that agents in the CIA probably are less than 6 degrees separated from Osama bin Laden, but because of tribal loyalties or threats of being killed, the last two links that could connect us to Osama, are not cooperative.

For the full NPR program, click here.

See related blog post “Make that at least 7 degrees of separation.”