An Even Smaller World

According to Wikipedia, the six degrees of separation is the idea that everyone is on average six steps away, by way of introduction, from any other person in the world, so that a chain of “a friend of a friend” statements can be made, on average, to connect any two people in six steps. Stanley Milgram’s famous “the small world experiment” examined the average path length for social networks of people in the Unite States. In their paper published in 1969, An Experimental Study of the Small World Program, Jeffrey Travers and Stanley Milgram arbitrarily selected individuals in Nebraska and Boston to generate acquaintance (or a friend of a friend) chains to a target person in Massachusetts. The experiment resulted in sixty-four chains to reach the target person; and within this group the mean number of intermediaries between starters and targets is 5.2 (6 hops).

In 2011, Facebook’s data science team found that our world may be even smaller then six degrees. Facebook’s data science team examined its then 721 million active Facebook users (with 69 billion friendships among them), and found that there was an average distance between 2 users was only 4.74 hops

99.6% of all pairs of users are connected by paths with 5 degrees (6 hops), and 92% of all pairs of users are connected by only four degrees (5 hops). When limiting the network analysis to a single country, most people are only separated by 3 degrees (4 hops).

A similar study was conducted by Sysomos in 2010 on Twitter’s social network. The researchers analyzed a corpus of 5.2 billion Twitter friendships, and found the most common friendship distance is 5 degrees of separation (with an average distance of 4.67 degrees). On average, about 50% of people on Twitter are only four steps away from each other, while nearly everyone is five steps away.

For further reading, check out:

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