I may be oversimplifying, but thinking of it at this extreme helped me intuit a bit better. Imagine 1,000,001 people. One of them is friends with the rest, all

I may be oversimplifying, but thinking of it at this extreme helped me intuit a bit better. Imagine 1,000,001 people. One of them is friends with the rest, all of whom only have this one friend. The average number of friends a person has is 2, but the aggregate average for their friends is 1,000,000. So most social graphs probably look like a spoke-hub where a minority of people have a very large number of friends.