Short e-mail chains reach targets worldwide.

Six degrees of separation--the notion that every person on the planet can reach every other through a chain of about six social ties--has been borne out by the first large-scale study of social networks.

The more than 24,000 e-mail users who participated in the study were randomly assigned one of 18 targets in 13 countries, including a police officer in Australia, a veterinarian in the Norwegian army, and a professor at an Ivy League university. The participants were asked to help relay a message to their target by forwarding it to just one acquaintance whom they regarded as "closer" than themselves to the target.

A total of 384 chains reached their target; the others fizzled out when, for example, a recipient mistook the message for spam or was too busy to forward it to a new person. The successful chains averaged 4.05 e-mails. Taking into account the lengths of the unsuccessful chains, researchers estimate that two strangers are typically connected to each other via five to seven e-mails, says Peter Sheridan Dodds, a member of the Columbia University team that performed the study.

"Through not very many links, people can actually find someone who is incredibly different from themselves on the other side of the world with a completely different job," Dodds says. "No one along the chain knows how the rest of the chain is functioning--they're all just doing something local, moving one step."

The study shows that the six-degrees idea, originally mooted in 1967 by social psychologist Stanley Milgram, is "not just an urban legend," says Steven Strogatz, a mathematician at Cornell University.

The Columbia team asked participants several questions, including how they chose the next recipient of the e-mail. The chains that succeeded in reaching their targets tended to contain many connections to casual acquaintances. The chains that failed relied more heavily on close friends.

This phenomenon, called the strength of weak ties, is not surprising, says Mark Granovetter, a sociologist at Stanford University. His research has shown that people typically find jobs through acquaintances rather than close friends.

"Your close friends tend to know each other, but your acquaintances tend to know people you don't know," he says. "They're much more your windows on the world."

Study participants usually chose to forward the message to someone closer to the target in location or profession rather than to simply send it to a friend who knew many people. This belies the widely held belief that hubs, individuals with many social ties, are crucial to the success of chains, the Columbia researchers note. Searching the social network is "largely an egalitarian exercise, not one whose success depends on a small minority of exceptional individuals," they say in the Aug. 8 Science.

It's likely, however, that the successful e-mail chains involved more hubs than the senders realized, Granovetter cautions. "The study doesn't prove that people with a lot of ties aren't important in the network," he says.

Although six degrees of separation seems like a small number of steps, in social terms it represents an enormous gulf, Strogatz says. "With the people who are two steps away from you, the friends of your friends, the connection is already getting a little hazy," he says. "Once the number is three, you have very little psychological connection to these people--they're three whole universes away.

"Six or seven steps is unfathomable," he adds. "It's meaningless socially."

The new research could be relevant for analyzing not just social ties but also peer-to-peer file sharing and computer networks, Dodds says.

The Columbia researchers have launched a new study in which participants may forward their message to many acquaintances instead of just one. The scientists are recruiting volunteers at the Web site www.smallworld.columbia.edu.