GraphTheory[RandomGraphs][RandomNetwork] - Maple Help

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GraphTheory[RandomGraphs][RandomNetwork]

Calling Sequence

RandomNetwork(n,p,options)

RandomNetwork(n,p,q,options)

RandomNetwork(V,p,options)

RandomNetwork(V,p,q,options)

Parameters

n

-

positive integer, larger than 1

p

-

real number between 0.0 and 1.0

V

-

list of vertices

q

-

real number between 0.0 and 1.0

options

-

sequence of options (see below)

Description

• 

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.

• 

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

• 

You can optionally specify q which is a real number 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.

• 

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

• 

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

Examples

withGraphTheory&colon;

withRandomGraphs&colon;

N:=RandomNetwork10&comma;0.5

N:=Graph 1: a directed unweighted graph with 10 vertices and 28 arc(s)

(1)

IsNetworkN

1&comma;10

(2)

DrawGraphN

N:=RandomNetworka&comma;b&comma;c&comma;d&comma;e&comma;0.5&comma;acyclic

N:=Graph 2: a directed unweighted graph with 5 vertices and 6 arc(s)

(3)

DrawNetworkN

N:=RandomNetwork10&comma;0.2&comma;acyclic&comma;weights&equals;1..5

N:=Graph 3: a directed weighted graph with 10 vertices and 31 arc(s)

(4)

WeightMatrixN

0100000000003132223000012010200000412024000001131400000052340000000025000000004200000000040000000000

(5)

MaxFlowN&comma;1&comma;10

1&comma;0100000000001000000000010000000000100000000001000000000010000000000010000000000000000000010000000000

(6)

See Also

AssignEdgeWeights, GraphTheory[DrawGraph], GraphTheory[DrawNetwork], GraphTheory[IsNetwork], GraphTheory[MaxFlow], RandomBipartiteGraph, RandomDigraph, RandomGraph, RandomTournament, RandomTree


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