Diameter of a graph

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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

Related graph properties