Radius of a graph

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Template:Undirected graph numerical invariant

Definition

The radius of a graph is defined for any connected graph as the radius 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 radius of a graph is the minimum, over all vertices, of the eccentricity of that vertex.

Note that for a finite graph, the radius is finite. For an infinite graph, the radius may be finite or .

For a graph that is not connected, we can consider the radius to be either or undefined.

Related invarants

Invariant Meaning Relation with radius
Diameter of a graph maximum of distances between pairs of vertices Radius Diameter Twice the radius