RandomGraph(n,p) creates an undirected unweighted graph on n vertices where each possible edge is present with probability p where 0.0 <= p <= 1.0.

RandomGraph(n,m) creates an undirected unweighted graph on n vertices and m edges where the m edges are chosen uniformly at random. The value of m must satisfy 0 <= m <= binomial(n,2) = n*(n-1)/2.

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.

If the option directed is specified, a random directed graph is chosen. This is equivalent to using the RandomDigraph command.

If the option connected is specified, the graph created is connected, and hence has at least n-1 edges. For RandomGraph(n,m,connected), m must be at least n-1. A random tree is first created, then the remaining m-n+1 edges are chosen uniformly at random. For RandomGraph(n,p,connected), a random tree is first created then each remaining edge is present with probability p.

If the option degree=d is specified, and d-regular n vertex graph is possible, then a random d-regular graph having n vertices will be returned. Note that this option cannot be present with the directed option. When this option is used the number of edges m may be omitted, but if provided must be consistent with the number of edges in a d-regular n vertex graph. This is equivalent to using the RandomRegularGraph command.

If the option weights=m..n is specified, where m <= n are integers, the graph is a weighted graph with integer 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.

f := proc() local x; x := U(); if x=1 then 1 else 2 fi end: