# Facebook Breaks Six Degrees of Separation Theory

Six degrees of separation is an idea that any two people on Earth, is on average, separated by no more than six intermediate connections so that a chain of "a friend of a friend" can be made to connect any two people in six steps or fewer. The idea was first proposed in 1929 in a short story by Hungarian author Frigyes Karinthy, and made popular by the John Guare play and movie, Six Degrees of Separation. Now researchers at Facebook and the University of Milan reported that the average number of acquaintances separating any two people in the world was not six but 4.74.

The theory of ‘Six Degrees of Separation’ was first put to the test by social psychologist Stanley Milgram in the 1960’s. Milgram selected 296 volunteers and asked them to send a message by postcard, through friends and then friends of friends, to a specific person in a Boston suburb. Milgram found that the average number of intermediate persons in these chains was 5.2 (representing about 6 hops), thereby cementing the ‘six degrees’ theory.

While Miligram’s experiment involved less than 300 individuals, the new research at the University of Milan used had a bigger sample – 721 million Facebook users, representing more than one-tenth of the world’s population.

The researchers used a set of algorithms developed at the University of Milan to calculate the average distance between any two people by computing a vast number of sample paths among Facebook users. The experiment took one month. They found that six degrees actually overstates the number of links between typical pairs of users.

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.

Thus, when considering even the most distant Facebook user in the Siberian tundra or the Peruvian rainforest, a friend of your friend probably knows a friend of their friend. When we limit our analysis to a single country, be it the US, Sweden, Italy, or any other, we find that the world gets even smaller, and most pairs of people are only separated by 3 degrees (4 hops).

Facebook also offered insight into some other metrics about the site. Only 10% of people have less than 10 friends, 20% have less than 25 friends, while 50% (the median) have over 100 friends. Meanwhile, because the distribution is highly skewed, the average friend count is 190. An important finding from our study, however, is that the distribution is not nearly as skewed as earlier studies of social networks have suggested.

A classic paradox regarding social networks dictates that, for most people, the median friend count of their friends is higher than their own friend count. On Facebook, that’s the case for 84% of our users. Why? Scott Feld wrote about this phenomenon in his 1991 paper Why Your Friends Have More Friends than You Do, showing that the same phenomenon dictates that college students typically find that their classes to be larger than the average class size, and that when sitting on an airplane, it will typically be more crowded than the average occupancy. These effects all arise because for people, classes, and flights to be popular, you must be much more likely to choose them. So you shouldn’t feel bad if it seems like all your friends are more popular than you: it appears this way to most of us.

Photo credit: BigStockPhoto

[via NYTimes]