My team and I wrote an app that will apply findings from a recent research paper to your Facebook graph. The app won’t post to your wall but it will show you both the shape of your friend network and which of your friends are most mathematically important to your life.

Instead of looking at a metric like the number of friends you have in common, this algorithm takes it a step further. It looks at how well connected your mutual friends are with each other, and suggests that having more diverse mutual friends indicates a stronger, more important relationship.

If everyone at work is connected via Facebook, then you will have many friends in common with your coworkers, but this doesn’t mean that these are your most important relationships. Since all of your common friends are within the same social circle, you know that these relationships are limited in scope.

But if you and a friend’s mutual connections include coworkers, college roommates, and cycling buddies, then you know that your relationship with this person spans many social circles, and they are more likely to be important to you. This also is effective at picking out romantic relationships.

There seemed to be issues with outliers when I tried it because there were a number of people with little or no mutual friends with very high scores, but in general the results were surprisingly accurate.

It’s also fun to look at the graph of your network and see the clusters of different social circles.