A simple example might help, along with the article.
Let’s suppose there are 12 people in our population. Two are social butterflies and are friends with everybody, so they have 11 friends each.
The other ten people are shy, and only become friends with the two people who approached them. They have 2 friends each.
For the ten shy people, they have 2 friends, but these two friends have 11 friends each. So, for ten people, they are less popular than their friends.
For the two social butterflies, they are more popular than their friends.
So, in this example, the odds are 10 in 12 (83%) that these people are less popular than their friends.