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 tot

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 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.