acyclic = truefalse

If the option acyclic is specified, a random acyclic network is created.

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 network 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 network is a weighted graph with numerical edge weights chosen from [x,y] uniformly at random.  The weight matrix W in the graph has datatype=float[8], that is, double precision floats (16 decimal digits), 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 network has datatype=anything, and if the edge from vertex i to j is not in the graph then W[i,j] = 0.

RandomNetwork(n,p) creates a directed unweighted network on n vertices. The larger p is, the larger the number of levels in the network.

RandomNetwork(V,p) does the same thing except that the vertex labels are chosen from the list V.

You can optionally specify q which is a numeric value between 0.0 and 1.0.  The result is a random network such that each possible arc is present with probability q. The default value for q is 0.5.

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

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

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

$N≔\mathrm{RandomNetwork}\left(10\,0.5\right)$

$N≔\mathrm{Graph\; 1:\; a\; directed\; graph\; with\; 10\; vertices\; and\; 28\; arc(s)}$

$\mathrm{IsNetwork}\left(N\right)$

$\left\{1\right\},\left\{10\right\}$

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

$N≔\mathrm{RandomNetwork}\left(\left[a\,b\,c\,d\,e\right]\,0.5\,\mathrm{acyclic}\right)$

$N≔\mathrm{Graph\; 2:\; a\; directed\; graph\; with\; 5\; vertices\; and\; 6\; arc(s)}$

$\mathrm{DrawNetwork}\left(N\right)$

$N≔\mathrm{RandomNetwork}\left(10\,0.2\,\mathrm{acyclic}\,\mathrm{weights}=1..5\right)$

$N≔\mathrm{Graph\; 3:\; a\; directed\; weighted\; graph\; with\; 10\; vertices\; and\; 31\; arc(s)}$

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

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

$\mathrm{MaxFlow}\left(N\,1\,10\right)$

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