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, a rational number, the edge probability (between 0 and 1)
- pq, a real number, 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 = {DBs, Dys, Ddk, DEc, Dko}

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.

Ways to use `generateRandomGraphs` :

"generateRandomGraphs(ZZ,ZZ)"
"generateRandomGraphs(ZZ,ZZ,QQ)"
"generateRandomGraphs(ZZ,ZZ,RR)"
"generateRandomGraphs(ZZ,ZZ,ZZ)"

For the programmer

The object generateRandomGraphs is a method function with options.