GraphRadius
GraphRadius[g]
gives the minimum eccentricity of the vertices in the graph g.
GraphRadius[{vw,…}]
uses rules vw to specify the graph g.
Details and Options
- The following options can be given:
-
EdgeWeight Automatic weight for each edge Method Automatic method to use - Possible Method settings include "Dijkstra", "FloydWarshall", and "Johnson".
Examples
open allclose allScope (7)
GraphRadius works with undirected graphs:
Use rules to specify the graph:
GraphRadius works with large graphs:
Applications (1)
Illustrate the radius in two Petersen graphs:
For a CompleteGraph, the radius is 1:
For a PathGraph of size 
, the radius is ![TemplateBox[{{n, /, 2}}, Floor]](Files/GraphRadius.en/3.png "TemplateBox[{{n, /, 2}}, Floor]"){kind=small}
:
For a CycleGraph of size 
, the radius is ![TemplateBox[{{n, /, 2}}, Floor]](Files/GraphRadius.en/5.png "TemplateBox[{{n, /, 2}}, Floor]"){kind=small}
:
For a WheelGraph, the radius is 1:
For a GridGraph of size {m,n}, the radius is ![TemplateBox[{{m, /, 2}}, Floor]+TemplateBox[{{n, /, 2}}, Floor]](Files/GraphRadius.en/6.png "TemplateBox[{{m, /, 2}}, Floor]+TemplateBox[{{n, /, 2}}, Floor]"){kind=small}
:
For a CompleteKaryTree tree of depth 
, the radius is 
:
Properties & Relations (1)
For a connected graph, the radius can be computed by VertexEccentricity:
Text
Wolfram Research (2010), GraphRadius, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphRadius.html (updated 2015).
CMS
Wolfram Language. 2010. "GraphRadius." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/GraphRadius.html.
APA
Wolfram Language. (2010). GraphRadius. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphRadius.html