# gmodel.ER: Observations from Erdos-Renyi random graph model In graphon: A Collection of Graphon Estimation Methods

## Description

Erdos-Renyi random graph model is one of the most popular and fundamental examples in modeling networks. Given n nodes, gmodel.ER generates edges randomly from Bernoulli distribution with a globally specified probability.

## Usage

 1 gmodel.ER(n, mode = "prob", par = 0.5, rep = 1) 

## Arguments

 n the number of nodes to be generated mode 'prob' (default) for edges to be drawn from Bernoulli distribution independently, or 'num' for a graph to have a fixed number of edges placed randomly par a real number \in [0,1] for mode='prob', or a positive integer \in [1, n*(n-1)/2] for mode='num' rep the number of observations to be generated.

## Details

In network science, 'ER' model is often interchangeably used in where we have fixed number of edges to be placed at random. The original use of edge-generating probability is from Gilbert (1959). Therefore, we set this algorithm to be flexible in that user can create either a fixed number of edges placed at random or set global edge-generating probability and draw independent observations following Bernoulli distribution.

## Value

depending on rep value, either

(rep=1)

an (n\times n) observation matrix, or

(rep>1)

a length-rep list where each element is an observation is an (n\times n) realization from the model.

## References

\insertRef

Erdos1959graphon

\insertRef

Gilbert1959graphon

## Examples

  1 2 3 4 5 6 7 8 9 10 11 ## Generate a graph of 100 nodes with a fixed number of edges graph1 = gmodel.ER(100,mode='num',par=100) image(graph1) ## Generate 3 graphs with a global with probability 0.5 graph2 = gmodel.ER(100,par=0.5,rep=3) par(mfrow=c(1,3)) image(graph2[[1]]) image(graph2[[2]]) image(graph2[[3]]) 

graphon documentation built on Sept. 21, 2018, 6:26 p.m.