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GraphTheory

 Center
 compute graph center
 Periphery
 compute graph periphery

 Calling Sequence Center(G, opts) Periphery(G, opts)

Parameters

 G - graph opts - (optional) one or more options as specified below

Options

 The options argument can contain one or more of the options shown below.
 • includevalue=true or false.
 This option specifies whether the extreme value (the minimum for Center and maximum for Periphery) should be returned with the corresponding set of indices. If true, an expression sequence is returned whose first element is the value and whose second element is the vertex set. If false (the default), the vertex set is returned.

Description

 • Center(G) computes the center of the graph G. This is the set of vertices of minimum eccentricity.
 • Periphery(G) computes the periphery of the graph G. This is the set of vertices of maximum eccentricity.
 • The minimum and maximum eccentricity values in G are known as the radius and diameter, respectively. These may be returned with the includevalue option.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $G≔\mathrm{Graph}\left(6,\left\{\left\{1,3\right\},\left\{1,6\right\},\left\{2,4\right\},\left\{2,6\right\},\left\{3,6\right\},\left\{4,5\right\},\left\{4,6\right\},\left\{5,6\right\}\right\}\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected graph with 6 vertices and 8 edge\left(s\right)}}$ (1)
 > $\mathrm{DrawGraph}\left(G\right)$
 > $\mathrm{Center}\left(G\right)$
 $\left\{{6}\right\}$ (2)
 > $\mathrm{Periphery}\left(G\right)$
 $\left\{{1}{,}{2}{,}{3}{,}{4}{,}{5}\right\}$ (3)

Compatibility

 • The GraphTheory[Center] and GraphTheory[Periphery] commands were introduced in Maple 2022.