# 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.

• If I name it, I might call it “largest isolation.” – Tsuyoshi Ito Apr 26 '11 at 17:29
• I was thinking "isolation distance". – Aryeh Apr 26 '11 at 17:34