Sample the hierarchical stochastic block model

Sampling from a hierarchical stochastic block model of networks.

Usage

sample_hierarchical_sbm(n, m, rho, C, p)

hierarchical_sbm(...)

Arguments

n

Integer scalar, the number of vertices.

m

Integer scalar, the number of vertices per block. n / m must be integer. Alternatively, an integer vector of block sizes, if not all the blocks have equal sizes.

rho

Numeric vector, the fraction of vertices per cluster, within a block. Must sum up to 1, and rho * m must be integer for all elements of rho. Alternatively a list of rho vectors, one for each block, if they are not the same for all blocks.

C

A square, symmetric numeric matrix, the Bernoulli rates for the clusters within a block. Its size must mach the size of the rho vector. Alternatively, a list of square matrices, if the Bernoulli rates differ in different blocks.

p

Numeric scalar, the Bernoulli rate of connections between vertices in different blocks.

...

Passed to sample_hierarchical_sbm().

Value

An igraph graph.

Details

The function generates a random graph according to the hierarchical stochastic block model.

See also

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_gnp(), sample_grg(), sample_growing(), 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

## Ten blocks with three clusters each
C <- matrix(c(
  1, 3 / 4, 0,
  3 / 4, 0, 3 / 4,
  0, 3 / 4, 3 / 4
), nrow = 3)
g <- sample_hierarchical_sbm(100, 10, rho = c(3, 3, 4) / 10, C = C, p = 1 / 20)
g
#> IGRAPH 00fb12a U--- 100 481 -- Hierarchical stochastic block model
#> + attr: name (g/c), m (g/n), rho (g/n), C (g/n), p (g/n)
#> + edges from 00fb12a:
#>  [1]  1-- 2  1-- 3  2-- 3  2-- 4  3-- 4  3-- 5  1-- 6  2-- 6  3-- 6  5-- 7
#> [11]  4-- 8  5-- 8  5-- 9  6-- 9  4--10  6--10  7-- 8  8-- 9  8--10 11--12
#> [21] 11--13 12--13 11--14 12--14 13--14 12--15 11--16 12--16 13--16 14--17
#> [31] 16--17 14--18 15--18 15--19 16--19 14--20 15--20 16--20 17--19 18--19
#> [41] 17--20 19--20 21--22 21--23 22--23 21--24 22--24 23--24 21--25 22--25
#> [51] 23--25 21--26 25--27 26--27 25--28 26--28 24--29 25--29 24--30 25--30
#> [61] 27--28 28--29 28--30 29--30 31--32 31--33 32--33 31--34 31--35 32--35
#> [71] 31--36 32--36 33--36 34--37 35--37 36--37 36--38 35--39 34--40 36--40
#> + ... omitted several edges
if (require(Matrix)) {
  image(g[])
}