The world is even smaller than you thought.

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.

Photo: Bloomberg

The experiment took one month. 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. They found that the average number of links from onearbitrarily selected person to another was 4.74. In the US, where more than half of the people over 13 are on Facebook, it was just 4.37.

“When considering even the most distant Facebook user in the Siberian tundra or the Peruvian rain forest," the company wrote on its blog, “a friend of your friend probably knows a friend of their friend".

The caveat there is “Facebook user"—like the Milgram study, the cohort was a self-selected group, in this case people with online access who use a particular website.

Though the study was by far the largest of its kind, it raised questions about definitions of terms like “friend" on Facebook.

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 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," Kleinberg said. “It’s the weak ties that make the world small."

Still, he noted that such ties were hardly meaningless.

The Facebook paper, titled Four Degrees of Separation, notes that Milgram posed both an optimistic interpretation of his findings and a pessimistic one.

On the one hand, it is a startling notion that reaching someone on the other side of the world takes only a small group of social connections.

On the other hand, Milgram said, it could also be evidence of psychological distance: that we were actually, on average, five “worlds apart".

“From this gloomier perspective," the paper says, “it is reassuring to see that our findings show that people are in fact only four worlds apart, and not five."

©2011/The New York Times