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GraphDiameter—Wolfram Language Documentation

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• See Also
  • VertexEccentricity
  • GraphRadius
  • GraphPeriphery
  • GraphCenter
  • GraphDistanceMatrix
• Related Guides
  • Paths, Cycles, and Flows
  • Graph Measures & Metrics
  • Graph Properties & Measurements

GraphDiameter[g]

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

Give the graph diameter for a complete graph:

GraphDiameter works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

GraphDiameter works with large graphs:

Illustrate the diameter in two Petersen graphs:

For a CompleteGraph, the diameter is 1:

For a PathGraph of size , the diameter is :

For a CycleGraph of size , the diameter is :

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

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

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

For a CompleteKaryTree tree of depth , the diameter is :

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

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

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

The graph diameter is unchanged when reversing every edge:

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