seed = integer or none

Seed for the random number generator. When an integer is specified, this is equivalent to calling randomize(seed).

weights = range or procedure

If the option weights=m..n is specified, where $m\le n$ are integers, the graph is a weighted graph with edge weights chosen from [m,n] uniformly at random.  The weight matrix W in the graph has datatype=integer, and if the edge from vertex i to j is not in the graph then W[i,j] = 0.

If the option weights=x..y where $x\le y$ are decimals is specified, the graph is a weighted graph with numerical edge weights chosen from [x,y] uniformly at random.  The weight matrix W in the graph ha and if the edge from vertex i to j is not in the graph then W[i,j] = 0.0.

If the option weights=f where f is a function (a Maple procedure) that returns a number (integer, rational, or decimal number), then f is used to generate the edge weights.  The weight matrix W in the graph has datatype=anything, and if the edge from vertex i to j is not in the graph then W[i,j] = 0.

RandomTournament(n) creates a random tournament on n vertices. This is a directed graph such that for every pair of vertices u and v either the arc u to v or the arc v to u is in the digraph.

If the first input is a positive integer n, then the vertices are labeled 1,2,...,n.  Alternatively you may specify the vertex labels in a list.

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

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

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

$T≔\mathrm{RandomTournament}\left(5\right)$

$T≔\mathrm{Graph\; 1:\; a\; directed\; graph\; with\; 5\; vertices\; and\; 10\; arc(s)}$

$T≔\mathrm{RandomTournament}\left(5\,\mathrm{weights}=1..5\right)$

$T≔\mathrm{Graph\; 2:\; a\; directed\; weighted\; graph\; with\; 5\; vertices\; and\; 10\; arc(s)}$

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

$\mathrm{true}$

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

$\left[\begin{array}{ccccc}0& 3& 0& 5& 2\\ 0& 0& 0& 0& 0\\ 3& 2& 0& 5& 0\\ 0& 1& 0& 0& 0\\ 0& 1& 4& 2& 0\end{array}\right]$