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

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.

Usage

sample_gnp(n, p, directed = FALSE, loops = FALSE)

gnp(...)

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().

Value

A graph object.

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).

Random graph models (games) erdos.renyi.game(), sample_(), sample_bipartite(), sample_chung_lu(), 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


# Random graph with expected mean degree of 2
g <- sample_gnp(1000, 2 / 1000)
mean(degree(g))
#> [1] 1.986
degree_distribution(g)
#>  [1] 0.125 0.289 0.277 0.167 0.091 0.033 0.015 0.002 0.000 0.001

# Pick a simple graph on 6 vertices uniformly at random
plot(sample_gnp(6, 0.5))