Yes, that’s what Facebook calculated on Friends Day. To celebrate its 12th birthday, Facebook decided to crunch its reams of data to figure out one of the most existential questions in the social networking world—how close are you to the rest of the world?

The answer: Only three-and-a-half people are needed for you to contact any other stranger on Earth, or at least among the 1.59 billion people active on Facebook.

b’Source: Wikimedia Commons’

But, how did Facebook come up with this?

Well, first they decoded this rather pretty but you-won’t-understand-what-it-says graph, which the social giant gave a cutesy name ‘Facebook Friend Graph’.

b’Facebook friend graph’

The analysis helped them come up with this number—3.57.

So, each person on Facebook is connected to every other person on the site by an average of three and a half other people, said Facebook on its blog.

Of course, between these two steps, the mathematical geniuses at Facebook had to use a lot of statistical techniques. If you understand terms like Flajolet-Martin algorithm and Apache Giraph, click here.

For the rest of us who’re mathematically challenged, here’s a simpler, though not entire, explanation. 

Let’s say you have 100 friends, and each one of them has a 100 friends. This means that in just a single ‘hop’, you are connected to 10,000 people (100 x 100). Now, if each of them has a 100 friends too, then in two ‘hops’, you can potentially know 10,00,000 people!

b’Source: Pixabay’

The calculations were a lot more complicated as Facebook had to do this for all its 1.59 billion users and quite a huge chunk of them had more than 200 friends. Also, many friends tend to overlap among known people.

But Facebook finally determined that you’re separated by only three-and-a-half degrees from every other person. In the US, people are a bit closer as the degree of separation is only 3.46.

In fact, the world has shrunk over the past five years. In 2011, Facebook had 721 million users and the degree of separation was 3.74. Now, with twice as many people on the social network, the distance between any two people in the world has shrunk.

So, the next time feel free to brag about how you know Mark Zuckerberg through someone, who knows someone, who knows someone.