There are only 3.57 degrees of separation: Facebook

How connected is the world? According to conventional wisdom, there are six degrees of separation between everyone on the planet. Based on the eponymous play—Six Degrees of Separation—written by John Guare in 1990, six degrees of separation explores the existential premise that everyone in the world is connected to everyone else in the world by a chain of no more than six acquaintances, thus, “six degrees of separation”.However, Menlo Park-based Facebook Inc. is challenging this theory, claiming that there are only three and a half degrees of separation. In its latest research the company did some number crunching to commemorate its 12th birthday that was also designated Friendship Day and determined that the average degree of separation between each person is only 3.57.This data is valid for Facebook’s 1.59 billion active users. The Friendship graph shows that the average distance observed is 4.57, corresponding to 3.57 intermediaries or “degrees of separation”.Interestingly, this statistic indicates not only the popularity of the social media network but also shows how the collective degrees of separation have shrunk over the past five years. Facebook conducted a similar exercise in 2011, along with researchers at Cornell, and the Università degli Studi di Milano, and computed that at that time Facebook’s 721 million users were separated by 3.74 degrees.

Five years later, with twice as many people using the social media site, we’ve grown more interconnected, thus shortening the distance between any two people in the world. So now the post shows that Facebook founder and chief executive officer Mark Zuckerberg’s average degree of separation from everyone is only 3.17, while chief operating officer Sheryl Sandberg’s is even less at 2.92 degrees of separation. The majority of the people on Facebook have averages between 2.9 and 4.2 degrees of separation.In its blog post, the company acknowledges that calculating this number across billions of people and hundreds of billions of friendship connections was a challenging exercise. Here is how they estimated the degrees of separation based on de-identified, aggregate data.

Imagine a person with 100 friends. If each of his friends also has 100 friends, then the number of friends-of-friends will be 10,000. If each of those friends-of-friends also has 100 friends then the number of friends-of-friends-of-friends will be 10,00,000. Some of those friends may overlap, so we need to filter down to unique connections. We’re only two degrees or hops away and the number is already big. In reality, this number grows even faster since most people on Facebook have more than 100 friends. And remember, the company needs to do this computation 1.6 billion times; that is, for every person on Facebook. Rather than calculate it exactly, the company relied on statistical algorithms to estimate distances with great accuracy, basically finding the approximate number of people within 1, 2, 3 degrees away from a source.In summary, Facebook finds that the world is more closely connected than you might think.


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