The concept of “six degrees of separation” is that any two humans are linked to each other by a mere five intermediaries, where each intermediary is an acquaintance of the other.

The theory of a limited number of degrees of separation was proposed in 1929 by the Hungarian writer Frigyes Karinthy in a short story called “Chains. In 1967 sociologist Stanley Milgram put the theory of limited degrees of separation to the test. He randomly selected people in Omaha, Nebraska and sent them packages. The packages contained information about a stranger in the Boston area. The information included the stranger’s name, location and occupation. The Nebraskans were asked to forward the package to someone they knew on a first-name basis who was most likely to know the stranger personally. And so on, until the package was delivered. Of the 300 packages sent out, 64 reached their targets with merely five intermediaries used on average. Amazing. How did this occur? And is the finding correct?

Since the Milgram study, many researchers have sliced and diced this idea of degrees of separation. They’ve studied it mathematically and have undertaken other experiments.

The math behind six-degrees is interesting. Assume you have 100 acquaintances. And each 100 acquaintances has 100 more. That is 10,000 people just in two steps. (The concept is show below in (a).) At step three there’s 1 million people and at four steps 100 million people. Thus, connecting in just a few steps seems very do-able. However, that is not how social networks work. Many of your 100 acquaintances know each other and their acquaintances know each other – triangles of connections are created. The diagram (b) below is closer to reality.

What has been found is that social networks are made up of many short links among friends and acquaintances and fewer random long links to people far away from most of main networks. It is these random, longer length connections that are important in connecting social networks and creating the small-world effect. For instance, Tammy and I have friends who a few years ago moved to Geneva, Switzerland. Now, the 100s of acquaintances we have are now linked to a social network in Switzerland.

What mathematical modeling of the six-degrees problem have shown is that it is the random long-link relationships (also known as “weak ties”) that really account for the phenomenon – its what creates links between social discrete social networks. A great way to visualize this point is to think of two small towns; the sort of towns where “everyone knows everyone else.” Now assume that Bob, a resident of town A moves to town B where after a few years is fully ingrained in that town’s social network. Now, most everyone in town A is connected with a mere one intermediary, Bob, to everyone in town B. The keys to having this close connectedness is (a) the close connections of people in the respective towns, and (b) having at least one connection between the towns (Bob).

A fascinating aspect of the “six-degrees” situation is that people are selecting who to connect to next rather than using all their contacts. Let me give an example. Say I know 100 people personally and I have been given the task to connect to an artist I do not know living in Brussels, Belgium. If I could pick one person to get closer to this artist it would probably be my friend Thomas who is from Brussels and moved to the U.S. to go to college and stayed. But, if I sent my request to all 100 of my friends it may be that my friend Amy who is an artist may have a better connection. Or that my friend James, unbeknownst to me, has a cousin who works at a cafe in Brussels that caters to artists. Maybe there is some other route that is optimal that I don’t know about. Thus, even if I can connect to the artist in Belgium in 5 steps, maybe I am really only 3 steps away.

Some notable follow-up studies:

In 2003, researchers from Columbia University found that the average number of steps required to connect two randomly selected people via email messages was between five and seven.

In 2006 Microsoft examined 30 billion electronic communications among 180 million various people. If people sent each other a direct message they were considered to know each other. Microsoft examined how many steps of acquaintances it would take to connect each and every person among the 180 million people. They found an average of 6.6 steps needed and that 78% of the connections could be made in less than 7 hops. The longest connections required 29 steps.

In 2016 a Facebook study found 4.57 steps on average between all its 1.6 billion.