Erdos-Renyi model

Generates a bernoulli random graph.

rgraph_er(
  n = 10,
  t = 1,
  p = 0.01,
  undirected = getOption("diffnet.undirected"),
  weighted = FALSE,
  self = getOption("diffnet.self"),
  as.edgelist = FALSE
)

Arguments

n

Integer. Number of vertices

t

Integer. Number of time periods

p

Double. Probability of a link between ego and alter.

undirected

Logical scalar. Whether the graph is undirected or not.

weighted

Logical. Whether the graph is weighted or not.

self

Logical. Whether it includes self-edges.

as.edgelist

Logical. When TRUE the graph is presented as an edgelist instead of an adjacency matrix.

Value

A graph represented by an adjacency matrix (if t=1), or an array of adjacency matrices (if t>1).

Details

For each pair of nodes \(\{i,j\}\), an edge is created with probability \(p\), this is, \(Pr\{Link i-j\} = Pr\{x<p\}\), where \(x\) is drawn from a \(Uniform(0,1)\).

When weighted=TRUE, the strength of ties is given by the random draw \(x\) used to compare against \(p\), hence, if \(x < p\) then the strength will be set to \(x\).

In the case of dynamic graphs, the algorithm is repeated \(t\) times, so the networks are uncorrelated.

Note

The resulting adjacency matrix is store as a dense matrix, not as a sparse matrix, hence the user should be careful when choosing the size of the network.

References

Barabasi, Albert-Laszlo. "Network science book" Retrieved November 1 (2015) https://barabasi.com/book/network-science.

See also

Other simulation functions: permute_graph(), rdiffnet(), rewire_graph(), rgraph_ba(), rgraph_ws(), ring_lattice()

Author

George G. Vega Yon

Examples

# Setting the seed
set.seed(13)

# Generating an directed graph
rgraph_er(undirected=FALSE, p = 0.1)
#> 10 x 10 sparse Matrix of class "dgCMatrix"
#>   [[ suppressing 10 column names ‘1’, ‘2’, ‘3’ ... ]]
#>                       
#> 1  . . . . . 1 . . . .
#> 2  . . . . . . . . . .
#> 3  . . . . . . . . . .
#> 4  . . . . . . 1 . . .
#> 5  . . . . . . . 1 . .
#> 6  1 . . . . . . . . 1
#> 7  . . . . . . . . . .
#> 8  . . . . . . . . . .
#> 9  . . . 1 . . . . . .
#> 10 . 1 . . . 1 . . 1 .

# Comparing P(tie)
x <- rgraph_er(1000, p=.1)
sum(x)/length(x)
#> [1] 0.099633

# Several period random gram
rgraph_er(t=5)
#> $`1`
#> 10 x 10 sparse Matrix of class "dgCMatrix"
#>   [[ suppressing 10 column names ‘1’, ‘2’, ‘3’ ... ]]
#>                       
#> 1  . . . . . . . . . .
#> 2  . . . 1 . . . . . .
#> 3  . . . . . . . . . .
#> 4  . . . . . . . . . .
#> 5  . . . . . . . . . .
#> 6  . . . . . . . . . .
#> 7  . . . . . . . . . 1
#> 8  . . . . . . . . . .
#> 9  . . . . . . . . . .
#> 10 . . . . . . . . . .
#> 
#> $`2`
#> 10 x 10 sparse Matrix of class "dgCMatrix"
#>   [[ suppressing 10 column names ‘1’, ‘2’, ‘3’ ... ]]
#>                       
#> 1  . . . . . . . . . .
#> 2  . . . . . . . . . .
#> 3  . . . . . . . . . .
#> 4  . . . . . . . . . .
#> 5  . . . . . . . . . .
#> 6  . . . . . . . . . .
#> 7  . . . . . . . . . .
#> 8  . . . . . . . . . .
#> 9  . . . . . . . . . .
#> 10 . . . . . . . . . .
#> 
#> $`3`
#> 10 x 10 sparse Matrix of class "dgCMatrix"
#>   [[ suppressing 10 column names ‘1’, ‘2’, ‘3’ ... ]]
#>                       
#> 1  . . . . . . . . . .
#> 2  . . . . . . . . . .
#> 3  . . . . . . . . . .
#> 4  1 . . . . . . . . .
#> 5  . . . . . . . . . .
#> 6  . . . . . . . . . .
#> 7  . . . . . . . . . .
#> 8  . . . . . . . . . .
#> 9  . . . . . . . . . .
#> 10 . . . . . . . . . .
#> 
#> $`4`
#> 10 x 10 sparse Matrix of class "dgCMatrix"
#>   [[ suppressing 10 column names ‘1’, ‘2’, ‘3’ ... ]]
#>                       
#> 1  . . . . . . . . . .
#> 2  . . . . . . . . . .
#> 3  . . . . . . . . . .
#> 4  . . . . . . . . . .
#> 5  . . . . . . . . . .
#> 6  . . . . . . . . . .
#> 7  . . . . . . . . . .
#> 8  . . . . . . . . . .
#> 9  . . . . . . . . . .
#> 10 . . . . . . . . . .
#> 
#> $`5`
#> 10 x 10 sparse Matrix of class "dgCMatrix"
#>   [[ suppressing 10 column names ‘1’, ‘2’, ‘3’ ... ]]
#>                       
#> 1  . . . . . . . . . .
#> 2  . . . . . . . . . .
#> 3  . . . . . . . . . .
#> 4  . . . . . . . . . 1
#> 5  . . . . . . . . . .
#> 6  . . . . . . . . . .
#> 7  . . . . . . . . . .
#> 8  . . . . . . . . . .
#> 9  . . . . . . . . . .
#> 10 . . . . . . . . . .
#> 
#> attr(,"undirected")
#> [1] FALSE