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THIS IS EITHER useful or terrifying, depending on how the data affect you: Researchers at Facebook and Cornell University have figured out a formula that predicts whether a couple is likely to break up within the next 60 days.

Jon Kleinberg, a computer scientist at Cornell, and Lars Backstrom, a senior engineer at Facebook, took a dataset of 1.3 million Facebook users who listed that they were in a relationship. They were actually looking for a formula that could predict which users were in relationships with each other.

They found that the shape, or “dispersion,” of your friends network is the key. You might expect that a cluster of mutual friends indicates two people are in a relationship but the opposite is the case: You’re more likely to have cluster of mutual coworkers listing each other as friends than a couple.

Instead, when two people have widely dispersed clusters that are linked mostly via the couple, that is the main predictor of whether you’re in a relationship. Here’s what it looks like:

Cornell University Library

In this diagram, “you” are at the center. The two dense clusters of friends are coworkers and college friends. The blue dot in the lower left is the significant other — he or she is at a remove from most of your friends but has links to many of them.

The dispersion formula makes it easier to guess who is in a relationship with whom.

But when the formula guesses incorrectly, that means a couple is more likely to break up soon, the researchers say:

We find that relationships on which recursive dispersion fails to correctly identify the partner are significantly more likely to transition to ‘single’ status over a 60- day period. This effect holds across all relationship ages and is particularly pronounced for relationships up to 12 months in age; here the transition probability is roughly 50% greater when recursive dispersion fails to recognise the partner.

Here’s what that looks like in a chart:

Cornell University Library

The red line shows incorrect guesses by the formula. When it fails to spot a couple based on dispersion, that couple has a much higher likelihood of breaking up within the next five months, the data suggest.

- Jim Edwards

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