# 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 [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-by-n)` observation matrix, or

(rep>1)

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

## References

Erdos, P. and Renyi, A. (1959) On Random Graphs I. Publications Mathematicae, Vol.6:290-297.

Gilbert, E.N. (1959) Random Graphs. Annals of Mathematical Statistics, Vol.30, No.4:1141-1144.

## 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 Nov. 17, 2017, 5:28 a.m.