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GraphTheory[RandomGraphs]

  

RandomTournament

  

generate random tournament

 

Calling Sequence

Parameters

Options

Description

Examples

Calling Sequence

RandomTournament(V,options)

RandomTournament(n,options)

Parameters

V

-

list of vertex labels

n

-

positive integer

options

-

(optional) equation(s) of the form option=value where option is one of seed or weights

Options

• 

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 <= 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 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.

Description

• 

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.

Examples

withGraphTheory&colon;

withRandomGraphs&colon;

TRandomTournament5

TGraph 1: a directed unweighted graph with 5 vertices and 10 arc(s)

(1)

TRandomTournament5&comma;weights=1..5

TGraph 2: a directed weighted graph with 5 vertices and 10 arc(s)

(2)

IsTournamentT

true

(3)

WeightMatrixT

0320000100000235100122000

(4)

See Also

AssignEdgeWeights

GraphTheory:-IsTournament

GraphTheory:-WeightMatrix

RandomBipartiteGraph

RandomDigraph

RandomGraph

RandomNetwork

RandomTree