# GraphDiameter

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:
•  EdgeWeight Automatic weight for each edge Method Automatic method to use
• With the default setting , 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".

# Examples

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## Basic Examples(1)

Give the graph diameter for a complete graph:

## Scope(7)

GraphDiameter works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

GraphDiameter works with large graphs:

## Applications(2)

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:

## Properties & Relations(3)

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: