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 1c9a3d3 U--- 10 28 --
#> + edges from 1c9a3d3:
#> [1] 1-- 3 1-- 4 1-- 7 1-- 8 1-- 9 1--10 2-- 4 2-- 6 2-- 9 3-- 4 3-- 5 3-- 6
#> [13] 3-- 9 4-- 5 4-- 6 4-- 7 4-- 8 4-- 9 4--10 5-- 6 5-- 8 5-- 9 5--10 6-- 7
#> [25] 6-- 8 6-- 9 6--10 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 3e6c512 U--- 20 139 --
#> + edges from 3e6c512:
#> [1] 1-- 2 1-- 6 1-- 7 1-- 8 1--10 1--11 1--12 1--13 1--15 1--16 1--17 1--18
#> [13] 1--20 2-- 4 2-- 5 2-- 6 2-- 7 2-- 8 2--10 2--14 2--15 2--17 2--19 3-- 4
#> [25] 3-- 5 3-- 7 3-- 8 3-- 9 3--10 3--11 3--12 3--13 3--14 3--15 3--17 3--19
#> [37] 3--20 4-- 5 4-- 6 4-- 8 4--11 4--12 4--13 4--14 4--15 4--16 4--18 4--19
#> [49] 4--20 5-- 6 5-- 8 5-- 9 5--11 5--12 5--13 5--14 5--15 5--18 5--19 6-- 8
#> [61] 6-- 9 6--13 6--14 6--16 6--17 6--18 6--19 6--20 7-- 9 7--10 7--12 7--13
#> [73] 7--14 7--15 7--16 7--17 7--18 7--19 7--20 8-- 9 8--10 8--11 8--15 8--16
#> [85] 8--18 8--19 8--20 9--10 9--11 9--12 9--13 9--14 9--15 9--16 9--17 9--18
#> [97] 9--19
#> + ... omitted several edges