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.