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GraphTheory[RandomGraphs]

  

RandomBipartiteGraph

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

RandomBipartiteGraph(n,p,options)

RandomBipartiteGraph(n,m,options)

RandomBipartiteGraph([a,b],p,options)

RandomBipartiteGraph([a,b],m,options)

Parameters

n, a, b

-

positive integers

p

-

real number between 0.0 and 1.0

m

-

non-negative integer

options

-

sequence of options (see below)

Description

• 

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

• 

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

• 

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

• 

If the option weights=m..n is specified, where m <= 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 <= 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.

• 

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

Examples

withGraphTheory&colon;

withRandomGraphs&colon;

GRandomBipartiteGraph10&comma;0.5

G:=Graph 1: an undirected unweighted graph with 10 vertices and 11 edge(s)

(1)

IsBipartiteG&comma;&apos;p&apos;

true

(2)

p

1&comma;2&comma;3&comma;4&comma;5&comma;6&comma;7&comma;8&comma;9&comma;10

(3)

GRandomBipartiteGraph2&comma;3&comma;1.0

G:=Graph 2: an undirected unweighted graph with 5 vertices and 6 edge(s)

(4)

NeighborsG

3&comma;4&comma;5&comma;3&comma;4&comma;5&comma;1&comma;2&comma;1&comma;2&comma;1&comma;2

(5)

GRandomBipartiteGraph2&comma;2&comma;4&comma;weights&equals;1..10

G:=Graph 3: an undirected weighted graph with 4 vertices and 4 edge(s)

(6)

WeightMatrixG

009700110910071000

(7)

HRandomBipartiteGraph7&comma;11&comma;45

H:=Graph 4: an undirected unweighted graph with 18 vertices and 45 edge(s)

(8)

ChromaticIndexH

9

(9)

See Also

AssignEdgeWeights

GraphTheory[ChromaticIndex]

GraphTheory[IsBipartite]

GraphTheory[Neighbors]

GraphTheory[WeightMatrix]

RandomDigraph

RandomGraph

RandomNetwork

RandomTournament

RandomTree

 


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