Generate random graphs according to the random dot product graph model
Source:R/games.R
sample_dot_product.RdIn 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.
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.
See also
sample_dirichlet(), sample_sphere_surface()
and sample_sphere_volume() for sampling position vectors.
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 csardi.gabor@gmail.com
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 49d3631 U--- 10 22 --
#> + edges from 49d3631:
#> [1] 1-- 2 1-- 3 1-- 5 2-- 3 2-- 5 2-- 7 2--10 3-- 4 3-- 6 3-- 9 3--10 4-- 5
#> [13] 4-- 6 4-- 7 4-- 8 5-- 6 5-- 7 5-- 8 5-- 9 6--10 7-- 8 7--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 dc132a0 U--- 20 135 --
#> + edges from dc132a0:
#> [1] 1-- 2 1-- 4 1-- 5 1-- 6 1-- 8 1-- 9 1--10 1--11 1--12 1--13
#> [11] 1--15 1--16 1--17 1--18 1--19 1--20 2-- 3 2-- 4 2-- 5 2--11
#> [21] 2--12 2--13 2--14 2--15 2--17 2--19 2--20 3-- 5 3-- 7 3-- 8
#> [31] 3-- 9 3--12 3--13 3--14 3--16 3--17 4-- 5 4-- 9 4--10 4--12
#> [41] 4--14 4--15 4--19 4--20 5-- 6 5-- 9 5--10 5--11 5--12 5--13
#> [51] 5--14 5--15 5--16 5--17 5--18 5--19 5--20 6-- 9 6--10 6--11
#> [61] 6--12 6--13 6--15 6--16 6--17 6--19 6--20 7-- 8 7-- 9 7--10
#> [71] 7--12 7--14 7--18 7--19 8-- 9 8--11 8--12 8--13 8--14 8--17
#> [81] 8--18 8--19 8--20 9--10 9--11 9--12 9--13 9--14 9--15 9--16
#> + ... omitted several edges