<p>Sloan calls this the "covering radius" when distributing points on a sphere.  <a href="http://www2.research.att.com/~njas/coverings/" rel="nofollow">http://www2.research.att.com/~njas/coverings/</a></p>

CC BY-SA 3.0
2011-04-26T18:11:29.387Z
Covering radius is slightly different because it is defined in terms of a metric space X and its (usually finite) subset S, whereas in this question there is only one metric space.
Tsuyoshi Ito
CC BY-SA 3.0
2011-04-26T17:47:45.717Z
2011-04-26T17:47:45.717Z
Jack
<p>Let $(X,d)$ be a metric space, and define $\rho$ to be the largest distance of any $x\in X$ to its nearest neighbor.</p>

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

<p>Does this quantity have a name? It's zero in continuous spaces and is only interesting in discrete ones.</p>

CC BY-SA 3.0
2011-04-26T17:29:01.200Z
If I name it, I might call it “largest isolation.”
Tsuyoshi Ito
CC BY-SA 3.0
2011-04-26T17:34:31.267Z
I was thinking "isolation distance".
Aryeh
<terminology><metric-spaces>
Need a term for a graph-theoretic/metric concept
Aryeh
# Need a term for a graph-theoretic/metric concept

(Asked by: username_0 on 2011-04-26)

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.

**Tags:** terminology, metric-spaces
> **Comments:**
> **username_1**: If I name it, I might call it “largest isolation.”  
> **username_0**: I was thinking "isolation distance".  

---

## 1 answers

### Answer by username_2 on 2011-04-26. Score: 2

Sloan calls this the "covering radius" when distributing points on a sphere. <http://www2.research.att.com/~njas/coverings/>

> **Comments:**
> **username_1**: Covering radius is slightly different because it is defined in terms of a metric space X and its (usually finite) subset S, whereas in this question there is only one metric space.  

---

