Lets say we have a graph $G$ with $|V|$ nodes. We wish to select $k$ such nodes while optimizing the following attribute:
maximize: for each $i$ and $j$, where $i \neq j$, $min(distance(v_i, v_j))$
Hope that makes sense. We'd like to pick $k$ nodes such that the distance between the closest pair of distinct nodes is maximal.
Currently, my plan is to pick a node in random, find the node furthest away from it $v_0$ and the one furthest away from that node $v_1$. Now recursively look for nodes such that maximize the minimal distance from the selected node set. Meaning, nodes that have the greatest distance possible from the any selected node and specifically the member closest to them of the previously selected set of nodes.
The issue with this is that it's greedy and therefore possibly very inaccurate.