weighted=truefalse

Specifies whether edge weights should be included in the calculation of weighted distance. The default is false.

Distance returns the number of edges in the shortest path from s to t. If no such path exists, the output is infinity.  The strategy is to use a breadth-first search (BFS).

To find a path from s to t with minimum distance use the ShortestPath command.

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

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

$P≔\mathrm{PetersenGraph}\left(\right)$

$P≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

$\mathrm{Distance}\left(P\,1\,4\right)$

$2$

$\mathrm{ShortestPath}\left(P\,1\,4\right)$

$\left[1\,5\,4\right]$

$\mathrm{DMP}≔\mathrm{Graph}\left(\mathrm{map}\left(x\mapsto \mathrm{sort}\left(\mathrm{convert}\left(x\,\mathrm{list}\right)\right)\,\mathrm{Edges}\left(P\right)\right)\right)$

$\mathrm{DMP}≔\mathrm{Graph\; 2:\; a\; directed\; unweighted\; graph\; with\; 10\; vertices\; and\; 15\; arc(s)}$

$\mathrm{Distance}\left(\mathrm{DMP}\,1\,4\right)$

$3$

$\mathrm{ShortestPath}\left(\mathrm{DMP}\,1\,4\right)$

$\left[1\,2\,3\,4\right]$

The GraphTheory[Distance] command was updated in Maple 2021.

The weighted option was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.