Suppose there are 7 billion people in the world and that the network (graph) of their friendships is connected. To guarantee no more than 6 degrees of separation between any two people, what is a lower bound on the number of friendships each person needs to have?
We have logx 7E9 = 6, or 7E9 = x6, or ⌈x⌉ = 44 friends.