# randomUniformHyperGraph -- returns a random uniform hypergraph

## Synopsis

• Usage:
H = randomUniformHyperGraph(R,c,d)
• Inputs:
• R, , which gives the vertex set of H
• c, an integer, the cardinality of the edge sets
• d, an integer, the number of edges in H
• Outputs:
• H, , a hypergraph with d edges of cardinality c on vertex set determined by R

## Description

This function allows one to create a uniform hypergraph on an underlying vertex set with a given number of randomly chosen edges of given cardinality.

 i1 : R = QQ[x_1..x_9]; i2 : randomUniformHyperGraph(R,3,4) o2 = HyperGraph{edges => {{x , x , x }, {x , x , x }, {x , x , x }, {x , x , x }}} 5 6 9 2 6 8 4 7 8 3 5 7 ring => R vertices => {x , x , x , x , x , x , x , x , x } 1 2 3 4 5 6 7 8 9 o2 : HyperGraph i3 : randomUniformHyperGraph(R,4,2) o3 = HyperGraph{edges => {{x , x , x , x }, {x , x , x , x }} } 2 3 4 9 2 3 4 8 ring => R vertices => {x , x , x , x , x , x , x , x , x } 1 2 3 4 5 6 7 8 9 o3 : HyperGraph

## Ways to use randomUniformHyperGraph :

• "randomUniformHyperGraph(PolynomialRing,ZZ,ZZ)"

## For the programmer

The object randomUniformHyperGraph is .