[LINK] "Why 'Six Degrees of Separation' Breaks Down Inside Cities"

[rfmcdonald]

At The Atlantic's City Lab, Laura Bliss describes the interesting ways in which the myth that all people can be united within "six degrees of separation" are wrong, at least in densely-populated urban areas.

You've probably heard of Stanley Milgram's famous "six degrees of separation" experiment: Subjects in the Midwest were each asked to send a package through the mail to a stranger in Boston, whom they could try to reach only by forwarding the package to other people they knew on a first-name basis. Milgram reported it took only five people for the package to pass from one stranger to another, thousands of miles apart.

The study inspired one of the most lasting theorems in the social sciences, but it's also been beset with criticism since its 1967 publication in Psychology Today: In an earlier, unpublished study, only five percent of packages made it to their targets, as psychologist Judith Kleinfeld reports. In published follow-ups, fewer than 30 percent of the packages reached their destinations.

In the years since, however, computational models have suggested that, despite his research, Milgram may have actually been correct. "If you ask a computer to figure out the degree of separation between two individuals all over the world, then you get the right number," says researcher Gábor Vattay of Eötvös Loránd University in Budapest. "You get six in the U.S. and a little more in other parts of the world."

But why, when humans are tasked with relaying packages, is there such a small success rate of reaching a destined stranger in six steps—or at all? And what happens to those lost packages? Alongside four colleagues, Gábor Vattay, a physicist and researcher in complex systems, published a paper this week in PLOS One which explores these questions, using an ocean of Twitter data and algorithm called "greedy routing"—meaning, in the case of package-forwarding, an algorithm that finds a route by choosing steps that get as close in physical space as possible to the destination.

About two and a half years ago, Vattay and his colleagues started collecting geo-located tweets, eventually amassing a database of about 6 million "nodes" (users linked to locations), and about 122 million "edges" (limits to the network of users). "A virtual map of human friendship," says Vattay. They then picked pairs of users from distant metropolitan areas. Using greedy routing, the researchers attempted to identify a path between the two users by forwarding messages via friends ("follow backs"), based on geographical proximity to the target user.

Greedy routing worked quite well on large scales. A message sent from a user in New York City and destined for a user in Chicago (a distance of a little over 1,000 miles) could reach the Chicago area in a single "hop." Indeed, the researchers found messages usually arrived within the city neighborhood of the target within three to six steps. But after that, "greedy routing" broke down. In only about 20 percent of cases could any path to a target be found, even though the network was fully connected. Inside a densely-populated city, spatial proximity loses its efficiency as a way of locating a person.