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The IsDirected(G) function returns true or false depending on whether the input graph is a directed or undirected graph.

The IsWeighted(G) function returns true if G is a weighted graph, and false otherwise.

To make a graph directed or weighted, use the MakeDirected or MakeWeighted commands.

To remove directions and weights from a graph, use the UnderlyingGraph command.

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

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

$G≔\mathrm{Graph\; 1:\; a\; directed\; graph\; with\; 3\; vertices\; and\; 3\; arcs}$

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

$\mathrm{true}$

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

$\mathrm{false}$

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

$\mathrm{K3}≔\mathrm{CompleteGraph}\left(3\right)$

$\mathrm{K3}≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 3\; vertices\; and\; 3\; edges}$

$\mathrm{IsDirected}\left(\mathrm{K3}\right)$

$\mathrm{false}$

$H≔\mathrm{Graph}\left(\left\{\left[\left\{1\,2\right\}\,2\right]\,\left[\left\{2\,3\right\}\,3\right]\right\}\right)$

$H≔\mathrm{Graph\; 3:\; an\; undirected\; weighted\; graph\; with\; 3\; vertices\; and\; 2\; edges}$

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

$\mathrm{true}$

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

$\left[\begin{array}{ccc}0& 2& 0\\ 2& 0& 3\\ 0& 3& 0\end{array}\right]$

$\mathrm{K3}≔\mathrm{CompleteGraph}\left(3\right)$

$\mathrm{K3}≔\mathrm{Graph\; 4:\; an\; undirected\; graph\; with\; 3\; vertices\; and\; 3\; edges}$

$\mathrm{IsWeighted}\left(\mathrm{K3}\right)$

$\mathrm{false}$

$\mathrm{K3}≔\mathrm{MakeWeighted}\left(\mathrm{K3}\right)$

$\mathrm{K3}≔\mathrm{Graph\; 5:\; an\; undirected\; weighted\; graph\; with\; 3\; vertices\; and\; 3\; edges}$

$\mathrm{IsWeighted}\left(\mathrm{K3}\right)$

$\mathrm{true}$

$\mathrm{WeightMatrix}\left(\mathrm{K3}\right)$

$\left[\begin{array}{ccc}0& 1& 1\\ 1& 0& 1\\ 1& 1& 0\end{array}\right]$