UnderlyingGraph - Maple Help

GraphTheory

 UnderlyingGraph
 construct underlying graph

 Calling Sequence UnderlyingGraph(G,opts)

Parameters

 G - graph opts - one or more options as specified below

Options

 • 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.
 • 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.
 • weights=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.

Description

 • 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)).

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $G≔\mathrm{Digraph}\left(\left\{\left[1,2\right],\left[2,3\right],\left[3,4\right],\left[4,1\right]\right\}\right)$
 ${G}{≔}{\mathrm{Graph 1: a directed unweighted graph with 4 vertices and 4 arc\left(s\right)}}$ (1)
 > $\mathrm{Edges}\left(G\right)$
 $\left\{\left[{1}{,}{2}\right]{,}\left[{2}{,}{3}\right]{,}\left[{3}{,}{4}\right]{,}\left[{4}{,}{1}\right]\right\}$ (2)
 > $\mathrm{Neighbors}\left(G\right)$
 $\left[\left[{2}{,}{4}\right]{,}\left[{1}{,}{3}\right]{,}\left[{2}{,}{4}\right]{,}\left[{1}{,}{3}\right]\right]$ (3)
 > $H≔\mathrm{UnderlyingGraph}\left(G\right):$
 > $\mathrm{Edges}\left(H\right)$
 $\left\{\left\{{1}{,}{2}\right\}{,}\left\{{1}{,}{4}\right\}{,}\left\{{2}{,}{3}\right\}{,}\left\{{3}{,}{4}\right\}\right\}$ (4)
 > $\mathrm{Neighbors}\left(H\right)$
 $\left[\left[{2}{,}{4}\right]{,}\left[{1}{,}{3}\right]{,}\left[{2}{,}{4}\right]{,}\left[{1}{,}{3}\right]\right]$ (5)

Compatibility

 • The GraphTheory[UnderlyingGraph] command was updated in Maple 2019.
 • The directed and weights options were introduced in Maple 2019.