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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.

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 1fa2423 U--- 100 433 -- Hierarchical stochastic block model
#> + attr: name (g/c), m (g/n), rho (g/n), C (g/n), p (g/n)
#> + edges from 1fa2423:
#>  [1]  1-- 2  1-- 3  2-- 3  1-- 4  3-- 4  1-- 5  2-- 5  3-- 5  1-- 6  2-- 6
#> [11]  3-- 6  4-- 7  5-- 7  6-- 7  4-- 8  5-- 8  6-- 8  5-- 9  4--10  5--10
#> [21]  6--10  8-- 9  7--10  8--10  9--10 11--12 11--13 12--13 11--14 13--14
#> [31] 11--15 13--15 12--16 13--16 14--17 15--17 16--17 14--18 15--18 16--18
#> [41] 14--19 15--19 14--20 15--20 17--20 18--20 21--22 21--23 22--23 21--24
#> [51] 22--24 23--24 21--25 22--25 23--25 24--27 25--27 26--27 24--28 25--28
#> [61] 26--28 26--29 25--30 26--30 27--28 27--29 28--29 29--30 31--32 31--33
#> [71] 32--33 31--34 32--34 33--34 31--36 33--36 34--37 35--37 36--37 34--38
#> + ... omitted several edges
if (require(Matrix)) {
  image(g[])
}