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(vecs, directed = FALSE)

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.

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.

dot_product_game()

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) bipartite_gnm(), 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 [email protected]

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 7f4a074 U--- 10 27 -- 
#> + edges from 7f4a074:
#>  [1] 1-- 2 1-- 5 1-- 6 1-- 7 1-- 8 1-- 9 1--10 2-- 3 2-- 5 2-- 6 2-- 9 2--10
#> [13] 3-- 4 3-- 6 3-- 7 3-- 9 4-- 7 4-- 8 4-- 9 4--10 5-- 7 5-- 8 6-- 9 6--10
#> [25] 7--10 8-- 9 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 f88be3f U--- 20 145 -- 
#> + edges from f88be3f:
#>   [1] 1-- 3 1-- 4 1-- 6 1-- 7 1-- 8 1--10 1--11 1--12 1--13 1--14 1--15 1--16
#>  [13] 1--18 1--19 1--20 2-- 3 2-- 5 2-- 6 2-- 7 2-- 8 2-- 9 2--10 2--11 2--12
#>  [25] 2--13 2--14 2--15 2--16 2--17 2--18 2--19 2--20 3-- 4 3-- 5 3-- 6 3-- 8
#>  [37] 3-- 9 3--10 3--11 3--12 3--13 3--14 3--16 3--17 3--18 4-- 6 4-- 7 4-- 8
#>  [49] 4--10 4--11 4--12 4--14 4--15 4--16 4--17 4--18 4--19 4--20 5-- 6 5-- 7
#>  [61] 5-- 8 5--10 5--11 5--12 5--13 5--14 5--15 5--16 5--17 5--19 5--20 6-- 8
#>  [73] 6-- 9 6--10 6--11 6--12 6--13 6--14 6--15 6--16 6--18 6--19 6--20 7-- 9
#>  [85] 7--10 7--11 7--12 7--14 7--15 7--16 7--17 7--18 7--19 8-- 9 8--10 8--11
#>  [97] 8--12 8--14 8--15 8--16 8--17 8--18 8--19 9--10 9--11 9--12 9--14 9--16
#> + ... omitted several edges