GraphTheory[RandomGraphs][RandomTree]
|
Calling Sequence
|
|
RandomTree(n)
RandomTree(n,degree<d)
RandomTree(n,options)
|
|
Parameters
|
|
n
|
-
|
positive integer or list of vertex labels
|
d
|
-
|
positive integer
|
options
|
-
|
sequence of options (see below)
|
|
|
|
|
Description
|
|
•
|
The RandomTree(n) command creates a random tree on n vertices. This is an undirected connected graph with n-1 edges. If the first input n is a positive integer, the vertices are labeled 1,2,...,n. Alternatively you may specify the vertex labels in a list.
|
•
|
Starting with the empty undirected graph T on n vertices, edges are chosen uniformly at random and inserted into T if they do do not create a cycle. This is repeated until T has n-1 edges.
|
•
|
The option degree<d or degree<=d limits the maximum degree of every vertex in the tree.
|
•
|
If the option weights=m..n is specified, where m <= n are integers, the tree 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 tree 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 tree 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
|
|
>
|
|
>
|
|
>
|
|
| (1) |
>
|
|
| (2) |
>
|
|
| (3) |
>
|
|
| (4) |
>
|
|
| (5) |
>
|
|
| (6) |
>
|
|
| (7) |
>
|
|
| (8) |
|
|
Download Help Document
Was this information helpful?