If G is a weighted graph, AssignEdgeWeights(G,...) assigns new random edge weights to G, that is, for each edge (i,j) in G the (i,j)th entry in the weight matrix of G is updated inplace.

If G is an unweighted graph, a weighted graph is first created before assigning the edge weights.  The structure of G is not copied.

AssignEdgeWeights(G,m..n) assigns the edges of the weighted graph random integer weights uniformly distributed on [m,n].

AssignEdgeWeights(G,a..b) assigns the edges of the weighted graph random decimal weights uniformly distributed on [a,b).

AssignEdgeWeights(G,R) assigns the edges of the weighted graph G values defined by R().  The Maple procedure R must return numerical values, that is, integers, rationals, or floating-point constants.

The random number generator used to compute the edge weights can be seeded using the seed option or the randomize function.

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

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

$T≔\mathrm{Graph}\left(\mathrm{weighted}\,\left\{\left[1\,2\right]\,\left[2\,3\right]\,\left[3\,4\right]\,\left[4\,1\right]\right\}\right)$

$T≔\mathrm{Graph\; 1:\; a\; directed\; weighted\; graph\; with\; 4\; vertices\; and\; 4\; arcs}$

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

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

$\mathrm{AssignEdgeWeights}\left(T\,1..9\right)$

$\mathrm{Graph\; 1:\; a\; directed\; weighted\; graph\; with\; 4\; vertices\; and\; 4\; arcs}$

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

$\left[\begin{array}{cccc}0& 4& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 7\\ 1& 0& 0& 0\end{array}\right]$

$T≔\mathrm{RandomTree}\left(4\right)$

$T≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 4\; vertices\; and\; 3\; edges}$

$T≔\mathrm{AssignEdgeWeights}\left(T\,0...1.0\right)$

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

$W≔\mathrm{WeightMatrix}\left(T\right)$

$W≔\left[\begin{array}{cccc}0.& 0.0975404049994095& 0.& 0.632359246225410\\ 0.0975404049994095& 0.& 0.& 0.\\ 0.& 0.& 0.& 0.913375856139019\\ 0.632359246225410& 0.& 0.913375856139019& 0.\end{array}\right]$

$\mathrm{op}\left(3\,W\right)$

$\mathrm{datatype}={\mathrm{float}}_8,\mathrm{storage}=\mathrm{rectangular},\mathrm{order}=\mathrm{Fortran\_order},\mathrm{shape}=\left[\mathrm{symmetric}\right]$

$T≔\mathrm{RandomTree}\left(100\right)$

$T≔\mathrm{Graph\; 4:\; an\; undirected\; graph\; with\; 100\; vertices\; and\; 99\; edges}$

$T≔\mathrm{AssignEdgeWeights}\left(T\,1..99\right)$

$T≔\mathrm{Graph\; 5:\; an\; undirected\; weighted\; graph\; with\; 100\; vertices\; and\; 99\; edges}$

$\mathrm{op}\left(3\,\mathrm{WeightMatrix}\left(T\right)\right)$

$\mathrm{datatype}=\mathrm{integer},\mathrm{storage}=\mathrm{sparse},\mathrm{order}=\mathrm{Fortran\_order},\mathrm{shape}=\left[\mathrm{symmetric}\right]$

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

$N≔\mathrm{Graph\; 6:\; a\; directed\; graph\; with\; 5\; vertices\; and\; 8\; arcs}$

$U≔\mathrm{rand}\left(1..4\right)\:$

B := proc() if U()=1 then 1 else 2 end if; end proc:

$N≔\mathrm{AssignEdgeWeights}\left(N\,B\right)$

$N≔\mathrm{Graph\; 7:\; a\; directed\; weighted\; graph\; with\; 5\; vertices\; and\; 8\; arcs}$

$W≔\mathrm{WeightMatrix}\left(N\right)$

$W≔\left[\begin{array}{ccccc}0& 1& 2& 1& 0\\ 0& 0& 1& 0& 1\\ 0& 0& 0& 0& 2\\ 0& 0& 1& 0& 2\\ 0& 0& 0& 0& 0\end{array}\right]$

$\mathrm{op}\left(3\,W\right)$

$\mathrm{datatype}=\mathrm{anything},\mathrm{storage}=\mathrm{rectangular},\mathrm{order}=\mathrm{Fortran\_order},\mathrm{shape}=\left[\right]$