BUILT-IN MATHEMATICA SYMBOL

GraphDiameter

GraphDiameter[g]
gives the maximum eccentricity of the vertices in the graph g.

Give the graph diameter for a complete graph:

Out[1]=

Out[2]=

GraphDiameter works with undirected graphs:

Directed graphs:

Weighted graphs:

Large graphs:

People at a family gathering:

Use Subsets to create edges between all members of the family:

The resulting social graph:

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

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:

The graph radius does change:

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

, the diameter is

:

For a CompleteKaryTree tree of depth

, the diameter is

: