directed=truefalse

Specifies whether directed edges should be permitted in the graph returned. If true, the result will be a directed graph if the input was directed. The default value, false, produces an undirected graph.

multigraph=truefalse

Specifies whether multiple edges should be included in the graph returned. If true, the result will contain any multiple edges present in the input. The default value, false, leaves only a single edge remaining in the output.

selfloops=truefalse

Specifies whether self-loops should be included in the graph returned. If true, the result will contain any self-loops present in the input. The default value, false, excludes all self-loops from the output.

weighted=truefalse

Specifies whether edge weights should be included in the graph returned. If true, the result will be a weighted graph if the input was weighted. The default value, false, produces an unweighted graph.

The UnderlyingGraph(G,opts) command returns an underlying graph of a graph.

The default behavior produces a graph in which the directions of arcs and the weights of the edges (or arcs) have been dropped.

Note that UnderlyingGraph(G) = Graph(Vertices(G), Neighbors(G)).

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

$G≔\mathrm{Digraph}\left(\left\{\left[1\,2\right]\,\left[2\,3\right]\,\left[3\,4\right]\,\left[4\,1\right]\right\}\right)$

$G≔\mathrm{Graph\; 1:\; a\; directed\; graph\; with\; 4\; vertices\; and\; 4\; arc(s)}$

$\mathrm{Edges}\left(G\right)$

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

$\mathrm{Neighbors}\left(G\right)$

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

$H≔\mathrm{UnderlyingGraph}\left(G\right)\:$

$\mathrm{Edges}\left(H\right)$

$\left\{\left\{1\,2\right\}\,\left\{1\,4\right\}\,\left\{2\,3\right\}\,\left\{3\,4\right\}\right\}$

$\mathrm{Neighbors}\left(H\right)$

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

The directed and weighted options were introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.

The selfloops option was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.

The GraphTheory[UnderlyingGraph] command was updated in Maple 2023.

The multigraph option was introduced in Maple 2023.

For more information on Maple 2023 changes, see Updates in Maple 2023.