Need a term for a graph-theoretic/metric concept Let $(X,d)$ be a metric space, and define $\rho$ to be the largest distance of any $x\in X$ to its nearest neighbor.

Formally,
$$ \rho = \sup_{x \in X}~ d(x, X \setminus \{x\}). $$

Does this quantity have a name? It's zero in continuous spaces and is only interesting in discrete ones.
Sloan calls this the "covering radius" when distributing points on a sphere.  http://www2.research.att.com/~njas/coverings/