Bipartite random graphs

Generate bipartite graphs using the Erdős-Rényi model

sample_bipartite(
  n1,
  n2,
  type = c("gnp", "gnm"),
  p,
  m,
  directed = FALSE,
  mode = c("out", "in", "all")
)

bipartite(...)

Arguments

n1

Integer scalar, the number of bottom vertices.

n2

Integer scalar, the number of top vertices.

type

Character scalar, the type of the graph, ‘gnp’ creates a \(G(n,p)\) graph, ‘gnm’ creates a \(G(n,m)\) graph. See details below.

p

Real scalar, connection probability for \(G(n,p)\) graphs. Should not be given for \(G(n,m)\) graphs.

m

Integer scalar, the number of edges for \(G(n,m)\) graphs. Should not be given for \(G(n,p)\) graphs.

directed

Logical scalar, whether to create a directed graph. See also the mode argument.

mode

Character scalar, specifies how to direct the edges in directed graphs. If it is ‘out’, then directed edges point from bottom vertices to top vertices. If it is ‘in’, edges point from top vertices to bottom vertices. ‘out’ and ‘in’ do not generate mutual edges. If this argument is ‘all’, then each edge direction is considered independently and mutual edges might be generated. This argument is ignored for undirected graphs.

...

Passed to sample_bipartite().

Value

A bipartite igraph graph.

Details

Similarly to unipartite (one-mode) networks, we can define the \(G(n,p)\), and \(G(n,m)\) graph classes for bipartite graphs, via their generating process. In \(G(n,p)\) every possible edge between top and bottom vertices is realized with probability \(p\), independently of the rest of the edges. In \(G(n,m)\), we uniformly choose \(m\) edges to realize.

See also

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

## empty graph
sample_bipartite(10, 5, p = 0)
#> IGRAPH ae1cecc U--B 15 0 -- Bipartite Gnp random graph
#> + attr: name (g/c), p (g/n), type (v/l)
#> + edges from ae1cecc:

## full graph
sample_bipartite(10, 5, p = 1)
#> IGRAPH 39172f8 U--B 15 50 -- Bipartite Gnp random graph
#> + attr: name (g/c), p (g/n), type (v/l)
#> + edges from 39172f8:
#>  [1]  1--11  1--12  1--13  1--14  1--15  2--11  2--12  2--13  2--14  2--15
#> [11]  3--11  3--12  3--13  3--14  3--15  4--11  4--12  4--13  4--14  4--15
#> [21]  5--11  5--12  5--13  5--14  5--15  6--11  6--12  6--13  6--14  6--15
#> [31]  7--11  7--12  7--13  7--14  7--15  8--11  8--12  8--13  8--14  8--15
#> [41]  9--11  9--12  9--13  9--14  9--15 10--11 10--12 10--13 10--14 10--15

## random bipartite graph
sample_bipartite(10, 5, p = .1)
#> IGRAPH 73ee7a6 U--B 15 6 -- Bipartite Gnp random graph
#> + attr: name (g/c), p (g/n), type (v/l)
#> + edges from 73ee7a6:
#> [1] 7--12 5--13 2--15 4--15 6--15 8--15

## directed bipartite graph, G(n,m)
sample_bipartite(10, 5, type = "Gnm", m = 20, directed = TRUE, mode = "all")
#> IGRAPH 64ca42d D--B 15 20 -- Bipartite Gnm random graph
#> + attr: name (g/c), m (g/n), type (v/l)
#> + edges from 64ca42d:
#>  [1]  2->11  8->11 10->11  1->12  7->12  4->13  7->13  6->14  4->15 10->15
#> [11] 15-> 1 12-> 2 13-> 2 15-> 2 11-> 3 12-> 3 13-> 4 15-> 6 12-> 7 15->10