Diameter of a graph
From Graph
Template:Undirected graph numerical invariant
Definition
The diameter of a graph is defined for any connected graph as the diameter of the metric space induced by it. Explicitly, for a graph 
with vertex set 
, it is:
where 
denotes the distance between two vertices. In words, the diameter of a graph is the maximum, over all vertices, of the eccentricity of that vertex.
Note that for a connected finite graph, the diameter is finite. For an infinite connected graph, the diameter may be finite or 
. A graph of finite diameter is a connected graph (finite or infinite) whose diameter is finite.
For a graph that is not connected, we can consider the diameter to be either or undefined.
Related invarants
| Invariant | Meaning | Relation with radius |
|---|---|---|
| Radius of a graph | minimum of eccentricities of vertices | Radius  Diameter Twice the radius
|
