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GraphDiameter[g]

gives the greatest distance between any pair of vertices in the graph g.

GraphDiameter[{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  
See Also
Related Guides
History
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GraphDiameter

GraphDiameter[g]

gives the greatest distance between any pair of vertices in the graph g.

GraphDiameter[{vw,…}]

uses rules vw to specify the graph g.

Details and Options

  • The following options can be given:
  • EdgeWeightAutomaticweight for each edge
    MethodAutomaticmethod to use
  • With the default setting EdgeWeight->Automatic, the edge weight of an edge is taken to be the EdgeWeight of the graph g if available; otherwise, it is 1.
  • Possible Method settings include "Dijkstra", "FloydWarshall", "Johnson", and "PseudoDiameter".
  • GraphDiameter works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples  (1)

Give the graph diameter for a complete graph:

Wolfram Language code: GraphDiameter[[image]]

Scope  (7)

GraphDiameter works with undirected graphs:

Wolfram Language code: GraphDiameter[[image]]

Directed graphs:

Wolfram Language code: GraphDiameter[[image]]

Weighted graphs:

Wolfram Language code: GraphDiameter[[image]]

Multigraphs:

Wolfram Language code: GraphDiameter[[image]]

Mixed graphs:

Wolfram Language code: GraphDiameter[[image]]

Use rules to specify the graph:

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

GraphDiameter works with large graphs:

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

Applications  (2)

Illustrate the diameter in two Petersen graphs:

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

For a CompleteGraph, the diameter is 1:

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

For a PathGraph of size , the diameter is :

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

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

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

For a WheelGraph of size 5 or more, the diameter is 2:

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

A WheelGraph of size 4 is a complete graph, so the diameter is 1:

Wolfram Language code: HighlightGraph[#, findDiameterPath[#]]&[WheelGraph[4, VertexSize -> Small]]

For a GridGraph of size {m,n}, the diameter is :

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

For a CompleteKaryTree tree of depth , the diameter is :

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

Find the largest number of steps separating two people at a family gathering network:

Wolfram Language code: g = ExampleData[{"NetworkGraph", "FamilyGathering"}]
Wolfram Language code: GraphDiameter[g]

Properties & Relations  (3)

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

Wolfram Language code: g = PetersenGraph[5, 2]
Wolfram Language code: GraphDiameter[g]
Wolfram Language code: Max[VertexEccentricity[g, #]& /@ VertexList[g]]

If a simple graph has diameter greater than 3, then its complement has diameter less than 3:

Wolfram Language code: g = GridGraph[{5, 5}]
Wolfram Language code: GraphDiameter[g] ≥ 3
Wolfram Language code: GraphDiameter[GraphComplement[g]] ≤ 3

The graph diameter is unchanged when reversing every edge:

Wolfram Language code: g = [image];
Wolfram Language code: h = ReverseGraph[g]
Wolfram Language code: {GraphDiameter[g], GraphDiameter[h]}
Wolfram Research (2010), GraphDiameter, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphDiameter.html (updated 2015).

Text

Wolfram Research (2010), GraphDiameter, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphDiameter.html (updated 2015).

CMS

Wolfram Language. 2010. "GraphDiameter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/GraphDiameter.html.

APA

Wolfram Language. (2010). GraphDiameter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphDiameter.html

BibTeX

@misc{reference.wolfram_2026_graphdiameter, author="Wolfram Research", title="{GraphDiameter}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GraphDiameter.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_graphdiameter, organization={Wolfram Research}, title={GraphDiameter}, year={2015}, url={https://reference.wolfram.com/language/ref/GraphDiameter.html}, note=[Accessed: 12-June-2026]}