The picture above depicts the shape of a random individual's Facebook network. Each dot represents a friend, and the lines connecting the dots represent mutual friendships. Can you figure out which dot is this user's romantic partner, just by looking at the diagram? Facebook can, according to The New York Times.

That's according to a new study by Jon Kleinberg, a computer scientist at Cornell University, and Lars Backstrom, a senior engineer at Facebook, which was recently published online.

The study had no problem with sample size; the researchers had access to a data set of 1.3 million randomly selected Facebook users aged 20 and up, each with 50 to 2,000 friends. All of the profiles sampled listed a spouse or romantic partner in their profile. If you crunch the math, that means the study had to account for roughly 379 million nodes and 8.6 billion links.

It found that the best indicator of romantic involvement was a network measure called high dispersion, which is what happens when a couple’s mutual friends are not well connected to one another. This might go against the grain of common intuition, but what this means is that the number of mutual friends that two people share is actually a weak predictor of whether they're in a relationship.

For example, if you look at the image at the top of the page again, you'll notice that there are two large clusters of connected friends at the top and on the right side of the diagram. The one at the top represents the user's co-workers and the one at the right is the user's old college friends. The user's spouse is contained in neither cluster. Rather, (s)he can be found in the lower left section. It's the node that appears isolated, but which connects many of the more remote dots of the diagram.

“A spouse or romantic partner is a bridge between a person’s different social worlds,” explained Kleinberg.

High dispersion wasn't always able to predict a user's spouse, but it was a surprisingly accurate predictor overall. It got the prediction correct 60 percent of the time, which is an absurdly high rate if you consider the number of false possibilities. Even if a user had no more than the minimum number of 50 friends, that's still just a 1 in 50 chance of getting it right. Of course, the odds are even steeper the more friends a user has.

Perhaps the most interesting result of the study, however, was what happened when the algorithm failed to accurately predict romantic involvement. When it got it wrong, it turned out to be a predictor that the user's relationship was in trouble. A couple in a declared relationship and without a high dispersion were 50 percent more likely to break up over the next two months than a couple with a high dispersion. In other words, it's possible that Facebook could predict the likelihood of your marriage ending in divorce before you even know it.

What the study ultimately seems to tell us about relationships is that the best ones are those that broaden our world. The ideal partner — the one most likely to stick around, anyway — is the one that connects you with networks of people who you might not otherwise have associated with. If a prospective partner is already embedded within a large cluster of mutual friends, then maybe there's less to be gained from becoming more than friends.

“We hadn’t had this view of it before,” admitted Kleinberg.

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