# Generate random graphs according to the \(G(n,p)\) Erdős-Rényi model

Source:`R/games.R`

`sample_gnp.Rd`

Every possible edge is created independently with the same probability `p`

.
This model is also referred to as a Bernoulli random graph since the
connectivity status of vertex pairs follows a Bernoulli distribution.

## Arguments

- n
The number of vertices in the graph.

- p
The probability for drawing an edge between two arbitrary vertices (\(G(n,p)\) graph).

- directed
Logical, whether the graph will be directed, defaults to

`FALSE`

.- loops
Logical, whether to add loop edges, defaults to

`FALSE`

.- ...
Passed to

`sample_gnp()`

.

## Details

The graph has `n`

vertices and each pair of vertices is connected
with the same probability `p`

. The `loops`

parameter controls whether
self-connections are also considered. This model effectively constrains
the average number of edges, \(p m_\text{max}\), where \(m_\text{max}\)
is the largest possible number of edges, which depends on whether the
graph is directed or undirected and whether self-loops are allowed.

## References

Erdős, P. and Rényi, A., On random graphs, *Publicationes
Mathematicae* 6, 290--297 (1959).

## See also

Random graph models (games)
`erdos.renyi.game()`

,
`sample_()`

,
`sample_bipartite()`

,
`sample_correlated_gnp()`

,
`sample_correlated_gnp_pair()`

,
`sample_degseq()`

,
`sample_dot_product()`

,
`sample_fitness()`

,
`sample_fitness_pl()`

,
`sample_forestfire()`

,
`sample_gnm()`

,
`sample_grg()`

,
`sample_growing()`

,
`sample_hierarchical_sbm()`

,
`sample_islands()`

,
`sample_k_regular()`

,
`sample_last_cit()`

,
`sample_pa()`

,
`sample_pa_age()`

,
`sample_pref()`

,
`sample_sbm()`

,
`sample_smallworld()`

,
`sample_traits_callaway()`

,
`sample_tree()`

## Author

Gabor Csardi csardi.gabor@gmail.com

## Examples

```
g <- sample_gnp(1000, 1 / 1000)
degree_distribution(g)
#> [1] 0.329 0.371 0.203 0.079 0.013 0.004 0.001
```