New York Times, JOHN MARKOFF and SOMINI SENGUPTA, November 21, 2011
Adding a new chapter to the research that cemented the phrase "six degrees of separation" into the language, scientists at Facebook and the University of Milan reported on Monday that the average number of acquaintances separating any two people in the world was not six but 4.74.
The original "six degrees" finding, published in 1967 by the psychologist Stanley Milgram, was drawn from 296 volunteers who were asked to send a message by postcard, through friends and then friends of friends, to a specific person in a Boston suburb.
The new research used a slightly bigger cohort: 721 million Facebook users, more than one-tenth of the world's population. The findings were posted on Facebook's site Monday night.
... A Microsoft study in 2008, using a more conservative definition of friend, found an average chain of 6.6 people in a group of 240 million who exchanged chat messages. Eric Horvitz, a Microsoft researcher who led the study in 2008, said that network was based on people who exchanged messages, rather than those who identified as "buddies."
"There is an issue of how many friends you actually have," he said. But, he said, the Internet might have altered the definition.
Jon Kleinberg, a computer science professor at Cornell and a faculty adviser to an author of the new study, said some links might be more meaningful than others.
He offered the example of a man wanted for a crime. A random Facebook user might discover that she took a class with someone who rented an apartment from someone who grew up with the suspect. They may all be connected as Facebook "friends."
"We are close, in a sense, to people who don't necessarily like us, sympathize with us or have anything in common with us," Dr. Kleinberg said. "It's the weak ties that make the world small."
Still, he noted that such ties were hardly meaningless. "We should ask what things spread well on weak ties," he said. "News spreads well on weak ties. Those people I met on vacation, if they send me some cool news, I might send that to my friends. If they send me something about a protest movement, I might not."
Here is Anatomy of Facebook post (Nov 21, 2011).
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.
To facilitate open access within the scientific community, Facebook made the papers available for download:
J. Ugander, B. Karrer, L. Backstrom, C. Marlow.
The Anatomy of the Facebook Social Graph,
L. Backstrom, P. Boldi, M. Rosa, J. Ugander, S. Vigna.
Four Degrees of Separation,