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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
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
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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

Examples

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Basic Examples  (1)

Give the graph radius for a complete graph:

Wolfram Language code: GraphRadius[[image]]

Scope  (7)

GraphRadius works with undirected graphs:

Wolfram Language code: GraphRadius[[image]]

Directed graphs:

Wolfram Language code: GraphRadius[[image]]

Weighted graphs:

Wolfram Language code: GraphRadius[[image]]

Multigraphs:

Wolfram Language code: GraphRadius[[image]]

Mixed graphs:

Wolfram Language code: GraphRadius[[image]]

Use rules to specify the graph:

Wolfram Language code: GraphRadius[{1 -> 2, 2 -> 3, 3 -> 1, 3 -> 4, 4 -> 5, 5 -> 3}]

GraphRadius works with large graphs:

Wolfram Language code: g = GridGraph[{10, 10, 10, 10}];
Wolfram Language code: GraphRadius[g]//Timing

Applications  (1)

Illustrate the radius in two Petersen graphs:

Wolfram Language code: findRadiusPath[g_ ? UndirectedGraphQ] := Module[{c = First@GraphCenter[g], d, v, pos}, d = Table[GraphDistance[g, c, u], {u, VertexList[g]}]; pos = First@Position[d, Max[d]]; v = First@Part[VertexList[g], pos]; PathGraph@FindShortestPath[g, c, v]]
Wolfram Language code: HighlightGraph[#, findRadiusPath[#]]& /@ {PetersenGraph[5, 2], PetersenGraph[6, 2]}

For a CompleteGraph, the radius is 1:

Wolfram Language code: HighlightGraph[#, findRadiusPath[#]]& /@ Table[CompleteGraph[n, VertexSize -> Small], {n, 3, 6}]

For a PathGraph of size , the radius is TemplateBox[{{n, /, 2}}, Floor]:

Wolfram Language code: HighlightGraph[#, findRadiusPath[#]]& /@ Table[PathGraph[Range[n], VertexSize -> Small], {n, 5, 8}]

For a CycleGraph of size , the radius is TemplateBox[{{n, /, 2}}, Floor]:

Wolfram Language code: HighlightGraph[#, findRadiusPath[#]]& /@ Table[CycleGraph[n, VertexSize -> Small], {n, 3, 6}]

For a WheelGraph, the radius is 1:

Wolfram Language code: HighlightGraph[#, findRadiusPath[#]]& /@ Table[WheelGraph[n, VertexSize -> Small], {n, 5, 8}]

For a GridGraph of size {m,n}, the radius is TemplateBox[{{m, /, 2}}, Floor]+TemplateBox[{{n, /, 2}}, Floor]:

Wolfram Language code: HighlightGraph[#, findRadiusPath[#]]& /@ Table[GridGraph[dim, VertexSize -> Small, ImageSize -> {Tiny, Tiny}], {dim, {{3, 3}, {3, 4}, {4, 3}, {4, 4}}}]

For a CompleteKaryTree tree of depth , the radius is :

Wolfram Language code: HighlightGraph[#, findRadiusPath[#]]& /@ Table[CompleteKaryTree[n, VertexSize -> Small], {n, 3, 5}]

Properties & Relations  (1)

For a connected graph, the radius can be computed by VertexEccentricity:

Wolfram Language code: g = GridGraph[{3, 4}]
Wolfram Language code: GraphRadius[g]
Wolfram Language code: Min[VertexEccentricity[g, #]& /@ VertexList[g]]
Wolfram Research (2010), GraphRadius, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphRadius.html (updated 2015).

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

BibTeX

@misc{reference.wolfram_2026_graphradius, author="Wolfram Research", title="{GraphRadius}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GraphRadius.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_graphradius, organization={Wolfram Research}, title={GraphRadius}, year={2015}, url={https://reference.wolfram.com/language/ref/GraphRadius.html}, note=[Accessed: 13-June-2026]}