Minimum number of people required to invite everyone to a reunion
One way to think about it is to make an undirected graph, and have every person be a vertex. There is an edge between two people if they are Facebook friends.

Now, assuming that you're asking people to invite their friends, and have those people invite their friends, and so on, then your problem basically boils down to finding the connected components of the graph you just made. (Two vertices are in the same connected component iff there exists a path between them)

Actually finding them isn't that bad; it's basically a slightly modified DFS.