This week Facebook announced that there are on average just 3.74 intermediate friends separating one user from another. They then stood back and waited for us all to be duly amazed. Well, let’s throw some numbers at the Facebook wall and see what sticks.
A few months ago I was on Facebook looking for a practitioner of pseudoscience whom I was in the process of annoying with facts (it’s a hobby of mine). When I eventually found them, Facebook kindly told me that we already had a friend in common. This came as no real surprise to me; through my desultory use of Facebook over the years I have somehow accrued 362 “friends”. If they all have a similar number of acquaintances, that could be more than 131 000 people within two steps from me. Sure, the social web is more tangled than that — each of my friends will not have 362 unique friends — but even taking overlaps into account, that’s a lot of “friends of friends” out there waiting to be encountered.
This concept of “degrees of separation” has been around since the early 20th century and many people have tried to measure what the actual average number of links is between any two people on Earth. Traditionally this has involved handing letters out to random people and seeing how many “passes” it takes to get them to a target individual. It was all a bit vague and the results far from robust.
Then everything changed with the arrival of the internet and millions of people started offering up all sorts of personal information about their friends. When Facebook took over from MySpace, it wasn’t the increased ease of sharing social information that got mathematicians excited, it was the sudden abundance of real-world data on worldwide social networks.
There’s nothing mathematicians like more than poking huge data sets. The researchers from the University of Milan analysed 721-million Facebook users and their friend networks. They found that 92% of people are linked by four intermediate friends and 99.6% of users are within five friends apart. Frankly, I’d like to see their research into what the remaining, “unconnected” 0.4% of users are even doing on Facebook. At least on Myspace they had their default friend “Tom”.
The area of mathematics known as “graph theory” looks at complicated networks and tries to understand their fundamental characteristics. While this is vital work when it comes to building robust computer networks, it does not tell us anything of great note about social degrees of separation. It’s not socially meaningful that a friend of your friends is buddies with an acquaintance of someone else’s pal. It’s just an innate feature of large, tangled networks.
So as much as I hate to maths on a parade, that isn’t actually very amazing. If everyone only had the median 100 friends this report found, that means you already have 10 000 friends of friends. If you include their 100 friends each, you’re at 1 million people within three degrees of separation. At five degrees of separation you have 10-billion people linked to you, which is greater than the Earth’s population.
If only having 100 friends each has you linked to everyone else on Earth an average 1.4 times each (so to speak), we shouldn’t be amazed that it’s a small world after all. We should be asking why we ever thought it was so big. —