Consider a social network with $n$ persons. Two persons $A$ and $B$ are said to be connected if either they are friends or they are related through a sequence of friends: that is, there exists a set of persons $F_1, \dots, F_m$ such that $A$ and $F_1$ are friends, $F_1$ and $F_2$ are friends, $\dots, F_{m−1}$ and $F_m$ are friends, and finally $F_m$ and $B$ are friends.
It is known that there are $k$ persons such that no pair among them is connected. What is the maximum number of friendships possible?