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Imagine the following scenario: You are provided a list of people in a conference, and you can see all of their Facebook friends. You want to know which people probably know each other. How can you do that in a way that is efficient?  Idea 0: If they are FB friends, then they are probably real life friends Right off the bat, you know that if somebody at the conference is Facebook friends with another person at the conference, then they're very likely to know each other. This is pretty quick to compute. You just build a map of conference goers to Facebook Friends, then go through all their Facebook Friends and check if they are a conference goer. However, now that we know who probably directly knows each other based on their Facebook friends, how can we figure out who might know each other at the conference but have not added each other on Facebook? Idea 1: Count the number of common Facebook friends One easy way to do this would be to say, for any two people, the more Facebook frie...