Create an undirected erdos renyi object

Create an undirected erdos renyi object

Usage

erdos_renyi(n, ..., p = NULL, poisson_edges = TRUE, allow_self_loops = TRUE)

Arguments

n

Number of nodes in graph.

...

Arguments passed on to undirected_factor_model

expected_degree

If specified, the desired expected degree of the graph. Specifying expected_degree simply rescales S to achieve this. Defaults to NULL. Do not specify both expected_degree and expected_density at the same time.

p

Probability of an edge between any two nodes. You must specify either p or expected_degree.

poisson_edges

Logical indicating whether or not multiple edges are allowed to form between a pair of nodes. Defaults to TRUE. When FALSE, sampling proceeds as usual, and duplicate edges are removed afterwards. Further, when FALSE, we assume that S specifies a desired between-factor connection probability, and back-transform this S to the appropriate Poisson intensity parameter to approximate Bernoulli factor connection probabilities. See Section 2.3 of Rohe et al. (2017) for some additional details.

allow_self_loops

Logical indicating whether or not nodes should be allowed to form edges with themselves. Defaults to TRUE. When FALSE, sampling proceeds allowing self-loops, and these are then removed after the fact.

Value

An undirected_factor_model S3 class based on a list with the following elements:

• X: The latent positions as a Matrix() object.

• S: The mixing matrix as a Matrix() object.

• n: The number of nodes in the network.

• k: The rank of expectation matrix. Equivalently, the dimension of the latent node position vectors.

See also

Other erdos renyi: directed_erdos_renyi()

Other undirected graphs: chung_lu(), dcsbm(), mmsbm(), overlapping_sbm(), planted_partition(), sbm()

Examples

set.seed(87)

er <- erdos_renyi(n = 10, p = 0.1)
er
#> Undirected Factor Model
#> -----------------------
#> 
#> Nodes (n): 10
#> Rank (k): 1
#> 
#> X: 10 x 1 [dgeMatrix] 
#> S: 1 x 1 [ddiMatrix] 
#> 
#> Poisson edges: TRUE 
#> Allow self loops: TRUE 
#> 
#> Expected edges: 10
#> Expected degree: 1
#> Expected density: 0.22222


er <- erdos_renyi(n = 10, expected_density = 0.1)
er
#> Undirected Factor Model
#> -----------------------
#> 
#> Nodes (n): 10
#> Rank (k): 1
#> 
#> X: 10 x 1 [dgeMatrix] 
#> S: 1 x 1 [ddiMatrix] 
#> 
#> Poisson edges: TRUE 
#> Allow self loops: TRUE 
#> 
#> Expected edges: 4
#> Expected degree: 0.4
#> Expected density: 0.1

big_er <- erdos_renyi(n = 10^6, expected_degree = 5)
big_er
#> Undirected Factor Model
#> -----------------------
#> 
#> Nodes (n): 1000000
#> Rank (k): 1
#> 
#> X: 1000000 x 1 [dgeMatrix] 
#> S: 1 x 1 [ddiMatrix] 
#> 
#> Poisson edges: TRUE 
#> Allow self loops: TRUE 
#> 
#> Expected edges: 5e+06
#> Expected degree: 5
#> Expected density: 1e-05

A <- sample_sparse(er)
A
#> 10 x 10 sparse Matrix of class "dsCMatrix"
#>                          
#>  [1,] . . . . . . . . . .
#>  [2,] . . . 1 . . . . . .
#>  [3,] . . . . . . . . . .
#>  [4,] . 1 . . . . . . . .
#>  [5,] . . . . . . . . . .
#>  [6,] . . . . . . . . . .
#>  [7,] . . . . . . . . . .
#>  [8,] . . . . . . . . . .
#>  [9,] . . . . . . . . . .
#> [10,] . . . . . . . . . .