## Friendship Paradox

https://en.wikipedia.org/wiki/Friendship_paradox

This article talks explains the “friendship paradox,” a strange result we get from graph theory. The friendship paradox says that your friends, on average, have more friends than you. While this initially seems nonsensical, the article explains it in two different ways. The first is a mathematical proof using an undirected graph showing that the average degree (amount of friends) of a friend is higher than the average degree of a random person (which could be you). While this math is a little complicated, there is an easier way to see that your friends are more popular than the average person. Since more popular people have more friends, they are more likely to be your friend. This is an example of sampling bias.

I find this very similar to Braess’ paradox, which we studied earlier in the semester, where adding a road to a highway system can create more traffic. It is also reminiscent of some mixed Nash equilibrium, which show that you want to use your more “powerful” option less frequently than your “weaker” option. All three of these show the usefulness of modeling these situations as a graph – you can get profound results by modeling networks. We only were able to prove the friendship paradox by using a graph modeling a social network, but we can extend this conclusion to other undirected graphs that we have seen, such as friends or Instagram followers, among others.