Generate random graphs according to the random dot product graph model

In this model, each vertex is represented by a latent position vector. Probability of an edge between two vertices are given by the dot product of their latent position vectors.

Usage

sample_dot_product(vecs, directed = FALSE)

dot_product(...)

Arguments

vecs: A numeric matrix in which each latent position vector is a column.
directed: A logical scalar, TRUE if the generated graph should be directed.
...: Passed to sample_dot_product().

Value

An igraph graph object which is the generated random dot product graph.

Details

The dot product of the latent position vectors should be in the [0,1] interval, otherwise a warning is given. For negative dot products, no edges are added; dot products that are larger than one always add an edge.

References

Christine Leigh Myers Nickel: Random dot product graphs, a model for social networks. Dissertation, Johns Hopkins University, Maryland, USA, 2006.

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

igraph_dot_product_game().

Examples


## A randomly generated  graph
lpvs <- matrix(rnorm(200), 20, 10)
lpvs <- apply(lpvs, 2, function(x) {
  return(abs(x) / sqrt(sum(x^2)))
})
g <- sample_dot_product(lpvs)
g
#> IGRAPH 046e8cb U--- 10 28 -- 
#> + edges from 046e8cb:
#>  [1] 1-- 3 1-- 4 1-- 6 1-- 7 1-- 9 1--10 2-- 4 2-- 5 2-- 8 2-- 9 3-- 4 3-- 5
#> [13] 3-- 7 3-- 8 3--10 4-- 5 4-- 6 4-- 7 4-- 8 4-- 9 5-- 7 5-- 8 5--10 6-- 8
#> [25] 6-- 9 6--10 7-- 8 8--10

## Sample latent vectors from the surface of the unit sphere
lpvs2 <- sample_sphere_surface(dim = 5, n = 20)
g2 <- sample_dot_product(lpvs2)
g2
#> IGRAPH ee77a7a U--- 20 142 -- 
#> + edges from ee77a7a:
#>  [1] 1-- 2 1-- 3 1-- 5 1-- 6 1-- 7 1-- 9 1--10 1--11 1--12 1--13 1--14 1--15
#> [13] 1--16 1--17 1--18 1--19 1--20 2-- 3 2-- 4 2-- 6 2-- 7 2--10 2--11 2--12
#> [25] 2--14 2--15 2--17 2--18 2--19 2--20 3-- 6 3-- 9 3--10 3--11 3--12 3--13
#> [37] 3--14 3--15 3--16 3--17 3--18 3--19 3--20 4-- 5 4-- 7 4-- 8 4--12 4--14
#> [49] 4--15 4--16 4--17 4--18 4--19 4--20 5-- 6 5-- 7 5-- 8 5--10 5--12 5--13
#> [61] 5--17 5--18 5--19 5--20 6-- 7 6-- 8 6-- 9 6--10 6--12 6--14 6--17 6--18
#> [73] 6--19 6--20 7-- 9 7--11 7--12 7--13 7--14 7--16 7--17 7--18 7--19 7--20
#> [85] 8-- 9 8--10 8--12 8--13 8--16 8--17 8--20 9--10 9--11 9--12 9--13 9--15
#> [97] 9--16 9--18 9--20
#> + ... omitted several edges