Question 17
A social network has $2025$ users. Two different users are either friends or not friends. A user is considered *lonely* if they have no friends. Initially, there are no lonely users, and two users Alice and Bob are not friends. A user may swap all their friends, meaning if they were friends with someone before the swap, they are no longer friends, and vice versa. Must there exist a way to arrange the $2025$ users in a sequence so that if, one-by-one in that sequence, each user swaps their friends, no user is ever lonely at any point during the process?