GetVertexPositions - Maple Help

GraphTheory

 GetVertexPositions
 get positions of graph vertices

 Calling Sequence GetVertexPositions(G, opts)

Parameters

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

Options

 • dimension=2 or 3
 The number of dimensions in the layout to return. The default is 2.
 • layout=default, bipartite, circle, fixed, grid, network, planar, random, spectral, spring, tree, or user.
 The layout option directs GetVertexPositions to return a previously computed layout with the specified layout method. The name style is a synonym for this option.
 If no layout method is specified, the vertex positions corresponding to the default drawing style of the graph are returned.
 • output=list or Matrix
 Specifies whether the points should be output as a list of lists or as a Matrix. The default is list.

Description

 • The GetVertexPositions('G', 'opts') command returns a list of coordinates representing the positions of the vertices in a previously computed layout.
 • If a layout is specified with the layout option and this layout was not previously computed, the empty list is returned.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $\mathrm{vp}≔\mathrm{GetVertexPositions}\left(\mathrm{CycleGraph}\left(9\right)\right)$
 ${\mathrm{vp}}{≔}\left[\left[{6.1232340}{×}{{10}}^{{-17}}{,}{1.}\right]{,}\left[{0.64278761}{,}{0.76604444}\right]{,}\left[{0.98480775}{,}{0.17364818}\right]{,}\left[{0.86602540}{,}{-0.50000000}\right]{,}\left[{0.34202014}{,}{-0.93969262}\right]{,}\left[{-0.34202014}{,}{-0.93969262}\right]{,}\left[{-0.86602540}{,}{-0.50000000}\right]{,}\left[{-0.98480775}{,}{0.17364818}\right]{,}\left[{-0.64278761}{,}{0.76604444}\right]\right]$ (1)
 > $G≔\mathrm{Graph}\left(\mathrm{Trail}\left(0,1,2,3,4,5,6,7,8,9,1\right),\mathrm{Trail}\left(4,0,7\right)\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 10 vertices and 12 edge\left(s\right)}}$ (2)
 > $\mathrm{SetVertexPositions}\left(G,\left[\left[0,0\right],\mathrm{op}\left(\mathrm{vp}\right)\right]\right):$
 > $\mathrm{DrawGraph}\left(G\right)$

We will disguise the Petersen graph by drawing it using the spring option and make those vertex positions the default.

 > $P≔\mathrm{PetersenGraph}\left(\right)$
 ${P}{≔}{\mathrm{Graph 2: an undirected unweighted graph with 10 vertices and 15 edge\left(s\right)}}$ (3)
 > $\mathrm{DrawGraph}\left(P,\mathrm{layout}=\mathrm{spring}\right)$
 > $S≔\mathrm{GetVertexPositions}\left(P,\mathrm{layout}=\mathrm{spring}\right)$
 ${S}{≔}\left[\left[{0.966139924305212}{,}{0.124423409473989}\right]{,}\left[{0.671492362648830}{,}{-0.622945284595226}\right]{,}\left[{0.0883553749810576}{,}{-0.911677655976657}\right]{,}\left[{-0.684646177755365}{,}{-0.692940942250190}\right]{,}\left[{0.0914644149940569}{,}{-0.184725679296864}\right]{,}\left[{0.285604708677752}{,}{1.}\right]{,}\left[{0.364102368397874}{,}{0.407906501760275}\right]{,}\left[{-0.268943385452634}{,}{0.543170254501320}\right]{,}\left[{-0.545132908598927}{,}{-0.0422890152843517}\right]{,}\left[{-0.968436682197856}{,}{0.379078411667707}\right]\right]$ (4)
 > $Q≔\mathrm{CopyGraph}\left(P\right)$
 ${Q}{≔}{\mathrm{Graph 3: an undirected unweighted graph with 10 vertices and 15 edge\left(s\right)}}$ (5)
 > $\mathrm{SetVertexPositions}\left(Q,S\right)$
 > $\mathrm{DrawGraph}\left(Q\right)$

Compatibility

 • The GraphTheory[GetVertexPositions] command was updated in Maple 2020.
 • The dimension, layout and output options were introduced in Maple 2020.