DrawPlanar displays the vertices and edges of a graph G as a Maple plot.

The algorithm used is Tutte's spring (or rubber) method. The vertices are placed on a face on a regular polygon, and the positions of the rest of the vertices are solved for such that each vertex is placed in the center of gravity of its neighbors.

Tutte's spring method works only for 3-connected graphs, so when the input graph is not 3-connected, strategies are employed to find a similar 3-connected graph (for example, 2-connected vertices are absorbed into the neighboring vertices).

The algorithm also finds a second drawing based on the first and chooses the one with the least "energy" for output.

Use of DrawPlanar can also be specified by a call to DrawGraph with option style=planar.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$\mathrm{G1}≔\mathrm{Graph}\left(\mathrm{Trail}\left(1\,2\,3\,4\,5\,6\,7\,8\,9\,10\,1\right)\,\mathrm{Trail}\left(11\,12\,6\,11\,1\,12\right)\right)$

$\mathrm{G1}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 12\; vertices\; and\; 15\; edges}$

$\mathrm{DrawPlanar}\left(\mathrm{G1}\right)$

$\mathrm{G2}≔\mathrm{SoccerBallGraph}\left(\right)$

$\mathrm{G2}≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 60\; vertices\; and\; 90\; edges}$

$\mathrm{DrawPlanar}\left(\mathrm{G2}\right)$