## Friendships

In the paper “Why your friends have more friends than you do” published in the American Journal of Sociology, Scott L. Feld demonstrates this seeming paradox. In his example, there are eight girls, whose mutual friendships are denoted by solid lines. While Betty has only one friend, Sue, Sue has four friends, Betty, Alice, Pam and Dale. The table in his paper summarizes the pattern of friendships among these friends. This shows that these eight girls have 2.5 friends on average. And the friends of these eight girls on average have 3 friends. The source of this paradox is that on average, you will tend to add friends of people who are popular because it’s a social game. According to a 2011 Pew survey, the average Facebook user has 245 friends, but the average friend on Facebook has 359 friends. This paradox is known as “friendship paradox”.

This phenomenon is related to what we have learned in the lecture. In the network of friendships, people represent nodes while pairs who are friend represent edges. There will be weak ties and strong ties between friends. The reasoning of the paradox Feld explains in his paper, also leads to a conclusion that almost everyone in the world is connected to each other. Because you are more likely to be friend with someone who has more friends than with someone who has fewer friends, that someone will also be friend with another one who has more friends than him. This will eventually result in a huge network with 0 or 1 giant component and/or dense cluster of networks. In fact, it is proven by the study of the Facebook social network by J. Ugander, B. Karrer, L. Backstrom and C. Marlow. They have determined that the Facebook social network is nearly fully connected, with 99.91% of individuals belonging to a single large connected component. Scott L. Feld has provided a real-life example of the networks among people.

http://www.jstor.org/stable/2781907