This is interesting, but given your parameters (predict the most friendships), all you're technically asking for is recall. I'll write an algorithm that has 100% recall: predict that all people become friends with each other.

If this is really a competition (and not just "Here, have fun with our dataset!"), you need to define the rules a little bit more clearly. How are you weighing recall vs. precision? Or are you just looking at % correct labels, where the only two labels possible are "FRIENDS" and "NOT FRIENDS"?