Facebook 'shrinks' six degrees of separation theory

Researchers at Facebook and the University of Milan reckon that the degrees of separation between any two people in the world have been reduced to 4.7 from social psychologist Stanley Milgram's "small world experiment" of six back in the '60s.

The study, which measured how many friends people have on Facebook, found that the notion of six degrees of separation had been shrinking over the past three years at the same time as the dominant social network bumped up its userbase.

It also noted, unsurprisingly, that many of those connections are localised. Which sounds a bit like the long-held scientific FACT that every showbiz star in Hollywood has a link to Footloose actor Kevin Bacon.

"We observed that while the entire world is only a few degrees away, a user’s friends are most likely to be of a similar age and come from the same country," said Facebook.

The company, alongside the researchers at the University of Milan, said it performed the study earlier this year when it "examined" all 721 million active Facebook users that represent a little over 10 per cent of the world population.

It said that there were 69 billion connections among the entire userbase.

Facebook also offered up an insight into some other metrics about the site, including revealing that half of its users had over 100 "friends" connections. Around 10 per cent, or 72 million people have 10 or fewer links to other users on the network.

The company was keen to stress that friend-shy people on the site needn't worry about their lack of connections.

"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," said the Mark Zuckerberg-run outfit.

"On Facebook, that’s the case for 84 per cent 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."

So that's alright then.

Of course, some might question Facebook's definition of friendship, given that connections are often only made online rather than in person, for example.

Pushing the arguments about the metrics adopted in the study to one side, the company said it used algorithms developed at the University of Milan to conduct the one-month-long test.

"We found that six degrees actually overstates the number of links between typical pairs of users: 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)," it said.

"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."

The company added that those hops reduced even more at a local level.

"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 three degrees (four hops)."

This isn't, however, the first such scrutiny of Milgram's original experiment.

Microsoft's research arm put it to the test in 2008 when it said it had proved the six degrees phenomenon using its own study.

Wonks at Redmond analysed messages sent by users of its instant messenger service in June 2006, the database for which was apparently stripped of identifying information.

That analysis yielded 180 billion pairs of users. Researchers concluded that 78 per cent of the pairs could be connected in seven hops or less, and that the average number of hops from one individual to another was 6.2. ®