({{, (RefLink[GraphRadius, paclet:ref/GraphRadius])[g] 
gives the minimum eccentricity of the vertices in the graph g.}, {, (RefLink[GraphRadius, paclet:ref/GraphRadius])[{v->w,…}]
uses rules v->w to specify the graph g.}})

OpenersNotesSection(Spacer1)Details

The following options can be given:

Possible (RefLink[Method, paclet:ref/Method]) settings include "Dijkstra", "FloydWarshall", and "Johnson".

OpenersPrimaryExamplesSection(Spacer1)Examples  (10)

OpenersExampleSection0(Spacer1)Basic Examples  (1)

Give the graph radius for a complete graph:

GraphRadius[]

OpenersExampleSection1(Spacer1)Scope  (7)

(RefLink[GraphRadius, paclet:ref/GraphRadius]) works with undirected graphs:

GraphRadius[]

Directed graphs:

GraphRadius[]

Weighted graphs:

GraphRadius[]

Multigraphs:

GraphRadius[]

Mixed graphs:

GraphRadius[]

Use rules to specify the graph:

GraphRadius[{1->2,2->3,3->1,3->4,4->5,5->3}]

(RefLink[GraphRadius, paclet:ref/GraphRadius]) works with large graphs:

g=GridGraph[{10,10,10,10}];

GraphRadius[g]//Timing

OpenersExampleSection3(Spacer1)Applications  (1)

Illustrate the radius in two Petersen graphs:

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]]

HighlightGraph[#,findRadiusPath[#]]&/@{PetersenGraph[5,2],PetersenGraph[6,2]}

For a (RefLink[CompleteGraph, paclet:ref/CompleteGraph]), the radius is 1:

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

For a (RefLink[PathGraph, paclet:ref/PathGraph]) of size n, the radius is (Floor[n/2]):

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

For a (RefLink[CycleGraph, paclet:ref/CycleGraph]) of size n, the radius is (Floor[n/2]):

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

For a (RefLink[WheelGraph, paclet:ref/WheelGraph]), the radius is 1:

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

For a (RefLink[GridGraph, paclet:ref/GridGraph]) of size {m,n}, the radius is (Floor[m/2])+(Floor[n/2]):

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

For a (RefLink[CompleteKaryTree, paclet:ref/CompleteKaryTree]) tree of depth n, the radius is n-1:

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

OpenersExampleSection4(Spacer1)Properties & Relations  (1)

For a connected graph, the radius can be computed by (RefLink[VertexEccentricity, paclet:ref/VertexEccentricity]):

g=GridGraph[{3,4}]

GraphRadius[g]

Min[VertexEccentricity[g,#]&/@VertexList[g]]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[VertexEccentricity, paclet:ref/VertexEccentricity])  ▪  (RefLink[GraphDiameter, paclet:ref/GraphDiameter])  ▪  (RefLink[GraphCenter, paclet:ref/GraphCenter])  ▪  (RefLink[GraphPeriphery, paclet:ref/GraphPeriphery])  ▪  (RefLink[GraphDistanceMatrix, paclet:ref/GraphDistanceMatrix])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Paths, Cycles, and Flows, paclet:guide/GraphPathsCyclesAndFlows])}, {▪(RefLinkPlain[Graph Measures & Metrics, paclet:guide/GraphMeasures])}, {▪(RefLinkPlain[Graph Properties & Measurements, paclet:guide/GraphPropertiesAndMeasurements])}})}})