# generateRandomGraphs -- generates random graphs on a given number of vertices

## Synopsis

• Usage:
G = generateRandomGraphs(n, num)
G = generateRandomGraphs(n, num, pq)
G = generateRandomGraphs(n, num, pz)
• Inputs:
• n, an integer, the number of vertices of the graphs, must be positive (see caveat)
• num, an integer, the number of random graphs to generate
• pq, , the edge probability (between 0 and 1)
• pq, , the edge probability (between 0 and 1)
• pz, an integer, the reciprocal of the edge probability (positive)
• Optional inputs:
• RandomSeed => an integer, default value null, the specified random seed is passed to nauty
• Outputs:
• G, a list, the randomly generated graphs

## Description

This method generates a specified number of random graphs with a given number of vertices. Note that some graphs may be isomorphic.

If the input pq is included, then the edges are chosen to be included with probability pq. If the input pz is included and is positive, then the edges are chosen to be included with probability 1/pz.

 ```i1 : generateRandomGraphs(5, 5, RandomSeed => 314159) o1 = {DEK, DbO, D[O, DiO, DMg} o1 : List``` ```i2 : generateRandomGraphs(5, 5) o2 = {DFS, DP_, Dg[, Ds[, DDS} o2 : List``` ```i3 : generateRandomGraphs(5, 5, RandomSeed => 314159) o3 = {DEK, DbO, D[O, DiO, DMg} o3 : List```

## Caveat

The number of vertices n must be positive as nauty cannot handle graphs with zero vertices. Further, if the probability pq is included, then it is rounded to a precision of one-hundred millionth.