The MakeWeighted command returns a graph with vertices and edges from G. If M is part of the input, then the edge weights are taken from it; otherwise edge weights are assumed to be 1. If G is undirected, then M is assumed to be a symmetric matrix.

For efficiency, use datatype=integer for wordsize integer weights and datatype=float[8] for numerical (decimal) edge weights.

To read or modify the edge weights of a weighted graph, use the GetEdgeWeight and SetEdgeWeight commands.

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

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

$G≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 3\; vertices\; and\; 3\; edge(s)}$

$M≔\mathrm{Matrix}\left(\left[\left[0\,2\,3\right]\,\left[2\,0\,1\right]\,\left[3\,1\,0\right]\right]\right)$

$M≔\left[\begin{array}{ccc}0& 2& 3\\ 2& 0& 1\\ 3& 1& 0\end{array}\right]$

$\mathrm{H1}≔\mathrm{MakeWeighted}\left(G\,M\right)$

$\mathrm{H1}≔\mathrm{Graph\; 2:\; an\; undirected\; weighted\; graph\; with\; 3\; vertices\; and\; 3\; edge(s)}$

$\mathrm{Edges}\left(\mathrm{H1}\right)$

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

$\mathrm{WeightMatrix}\left(\mathrm{H1}\right)$

$\left[\begin{array}{ccc}0& 2& 3\\ 2& 0& 1\\ 3& 1& 0\end{array}\right]$

$M≔\mathrm{Matrix}\left(M\,\mathrm{datatype}=\mathrm{float}\left[8\right]\,\mathrm{shape}=\mathrm{symmetric}\right)$

$M≔\left[\begin{array}{ccc}0.& 2.& 3.\\ 2.& 0.& 1.\\ 3.& 1.& 0.\end{array}\right]$

$\mathrm{H2}≔\mathrm{MakeWeighted}\left(G\,M\right)$

$\mathrm{H2}≔\mathrm{Graph\; 3:\; an\; undirected\; weighted\; graph\; with\; 3\; vertices\; and\; 3\; edge(s)}$

$\mathrm{WeightMatrix}\left(\mathrm{H2}\right)$

$\left[\begin{array}{ccc}0.& 2.& 3.\\ 2.& 0.& 1.\\ 3.& 1.& 0.\end{array}\right]$