# Three and a half degrees of separation

Sergey Edunov, Carlos Greg Diuk, Ismail Onur Filiz, Smriti Bhagat, and Moira Burke at Facebook Research: “How connected is the world? Playwrights, poets, and scientists have proposed that everyone on the planet is connected to everyone else by six other people. In honor of Friends Day, we’ve crunched the Facebook friend graph and determined that the number is 3.57. Each person in the world (at least among the 1.59 billion people active on Facebook) is connected to every other person by an average of three and a half other people. The average distance we observe is 4.57, corresponding to 3.57 intermediaries or “degrees of separation.” Within the US, people are connected to each other by an average of 3.46 degrees.

Our collective “degrees of separation” have shrunk over the past five years. In 2011, researchers at Cornell, the Università degli Studi di Milano, and Facebook computed the average across the 721 million people using the site then, and found that it was 3.74 [4,5]. Now, with twice as many people using the site, we’ve grown more interconnected, thus shortening the distance between any two people in the world.

Calculating this number across billions of people and hundreds of billions of friendship connections is challenging; we use statistical techniques described below to precisely estimate distance based on de-identified, aggregate data….

The majority of the people on Facebook have averages between 2.9 and 4.2 degrees of separation. Figure 1 (below) shows the distribution of averages for each person.

Figure 1. Estimated average degrees of separation between all people on Facebook. The average person is connected to every other person by an average of 3.57 steps. The majority of people have an average between 3 and 4 steps….(More)”