least cpu-expensive way to find the two most (and least) remote vertices of a graph [igraph]
For the first question, you can find all shortest paths, and then choose between the pairs making up the longest distances.
I don't really understand the second question. If you are searching for unweighted paths, then every pair of vertices at both ends of an edge have the minimum distance (1). That is, if you don't consider paths to the vertices themselves, these have length zero, by definition.
In igraph, what's the least cpu-expensive way to find:

the two most remote vertices (in term of shortest distances form one another) of a graph. Unlike the farthest.points() function, which chooses the first found pair of vertices with the longest shortest distance if more than one pair exists, I'd like to randomly select this pair.
same thing with the closest vertices of a graph.

Thanks!