The ReverseGraph( G ) command constructs the reverse graph of the graph G. The reverse graph is a graph with the same vertices as G but with the directions of all edges reversed.

This operation defined on all graphs but only gives meaningful results for directed graphs.

This operation is also known as the transpose graph or converse graph. The adjacency matrix of ReverseGraph(G) is the transpose of the adjacency matrix of G.

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

$G≔\mathrm{Graph}\left(6\,\left\{\left[1\,2\right]\,\left[2\,3\right]\,\left[2\,4\right]\,\left[4\,5\right]\right\}\right)$

$G≔\mathrm{Graph\; 1:\; a\; directed\; graph\; with\; 6\; vertices\; and\; 4\; arc(s)}$

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

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

$H≔\mathrm{Graph\; 2:\; a\; directed\; graph\; with\; 6\; vertices\; and\; 4\; arc(s)}$

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

$\mathbf{use}\mathrm{LinearAlgebra}\mathbf{in}\mathrm{Equal}\left(\mathrm{AdjacencyMatrix}\left(H\right)\,\mathrm{Transpose}\left(\mathrm{AdjacencyMatrix}\left(G\right)\right)\right)\mathbf{end\; use}$

$\mathrm{true}$

The GraphTheory[ReverseGraph] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.