directed = truefalse

Specifies whether the graph should be directed. The default is false.

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 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 graph has datatype=anything, and if the edge from vertex i to j is not in the graph then W[i,j] = 0.

RandomBipartiteGraph(n, p) creates an unweighted bipartite graph on n vertices where each possible edge is present with probability p.

RandomBipartiteGraph(n, m) creates an unweighted bipartite graph on n vertices and m edges where the m edges are chosen uniformly at random.

RandomBipartiteGraph([a,b], p) creates an unweighted bipartite graph on a+b vertices with partite sets of sizes a and b, where each possible edge is present with probability p.

RandomBipartiteGraph([a,b], m) creates an unweighted bipartite graph on a+b vertices with partite sets of sizes a and b, and with m edges chosen uniformly at random.

By default, the created bipartite graph is undirected. If the option directed or directed=true is given, the resulting graph is directed.

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

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

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

$G≔\mathrm{RandomBipartiteGraph}\left(10\,0.5\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 8\; edge(s)}$

$\mathrm{IsBipartite}\left(G\,'p'\right)$

$\mathrm{true}$

$p$

$\left[\left[1\,2\,3\,4\,5\,6\,7\right]\,\left[8\,9\,10\right]\right]$

$G≔\mathrm{RandomBipartiteGraph}\left(\left[2\,3\right]\,1.0\right)$

$G≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 5\; vertices\; and\; 6\; edge(s)}$

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

$\left[\left[3\,4\,5\right]\,\left[3\,4\,5\right]\,\left[1\,2\right]\,\left[1\,2\right]\,\left[1\,2\right]\right]$

$G≔\mathrm{RandomBipartiteGraph}\left(\left[2\,2\right]\,4\,\mathrm{weights}=1..10\right)$

$G≔\mathrm{Graph\; 3:\; an\; undirected\; weighted\; graph\; with\; 4\; vertices\; and\; 4\; edge(s)}$

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

$\left[\begin{array}{cccc}0& 0& 6& 7\\ 0& 0& 7& 9\\ 6& 7& 0& 0\\ 7& 9& 0& 0\end{array}\right]$

$H≔\mathrm{RandomBipartiteGraph}\left(\left[7\,11\right]\,45\right)$

$H≔\mathrm{Graph\; 4:\; an\; undirected\; graph\; with\; 18\; vertices\; and\; 46\; edge(s)}$

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

$8$

The GraphTheory[RandomGraphs][RandomBipartiteGraph] command was updated in Maple 2021.

The directed option was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.