You're exactly right - [argh] it's not at all the traveling salesman problem. Thanks for the correction.
In any case, the thesis of my post was that it's a totally solvable problem and that you could use other factors to reduce the number of nodes - like looking for shared group or network memberships.
I think this is the relavant bit? http://en.wikipedia.org/wiki/Dijkstra's_algorithm Except that the Facebook thing wouldn't be a weighted graph - unless you wanted to consider length of time people have been marked as friends, or count "worked together" more or less than some other form of association.
In any case, the thesis of my post was that it's a totally solvable problem and that you could use other factors to reduce the number of nodes - like looking for shared group or network memberships.
I think this is the relavant bit? http://en.wikipedia.org/wiki/Dijkstra's_algorithm Except that the Facebook thing wouldn't be a weighted graph - unless you wanted to consider length of time people have been marked as friends, or count "worked together" more or less than some other form of association.