In 1991 sociologist Scott Feld wrote a scientific paper entitled “Why your friends have more friends than you do.”1 Strange title for a paper, particularly because most of us do not perceive ourselves as any less popular than our friends. But according to Feld, if we could count the number of friends our friends have, most of us would find we come up short. Indeed, in any social group it can be proven that the average number of friends of friends is larger than or equal to the average number of friends; the equality holds only for the special case in which every person has exactly the same number of friends.
Far from a mere curiosity, this apparent friendship paradox is intimately related to the percolation properties of networks. For example, if a contagious disease propagates through a social network, one way to curb the spread would be to...
