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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.

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 70af1bc U--- 10 23 -- 
#> + edges from 70af1bc:
#>  [1] 1-- 2 1-- 3 1-- 6 1-- 7 2-- 3 2-- 5 2-- 7 2-- 8 2-- 9 3-- 4 4-- 5 4-- 6
#> [13] 4-- 8 4--10 5-- 6 5--10 6-- 7 6-- 9 6--10 7-- 9 8-- 9 8--10 9--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 fd3c116 U--- 20 131 -- 
#> + edges from fd3c116:
#>  [1] 1-- 3 1-- 4 1-- 6 1-- 7 1-- 8 1-- 9 1--10 1--11 1--12 1--13 1--14 1--15
#> [13] 1--18 1--20 2-- 3 2-- 4 2-- 5 2-- 6 2-- 7 2-- 9 2--10 2--13 2--15 2--16
#> [25] 2--17 2--18 2--20 3-- 4 3-- 5 3-- 6 3-- 7 3-- 8 3-- 9 3--10 3--11 3--12
#> [37] 3--13 3--14 3--15 3--16 3--18 3--20 4-- 6 4-- 7 4-- 8 4-- 9 4--10 4--12
#> [49] 4--13 4--14 4--16 4--17 4--18 4--19 4--20 5-- 7 5-- 9 5--10 5--12 5--13
#> [61] 5--16 5--17 5--18 5--19 5--20 6-- 7 6-- 8 6-- 9 6--10 6--11 6--12 6--13
#> [73] 6--14 6--16 6--17 6--19 6--20 7-- 9 7--10 7--12 7--13 7--14 7--15 7--16
#> [85] 7--17 7--18 8--10 8--11 8--12 8--13 8--15 8--16 8--19 9--10 9--12 9--13
#> [97] 9--15 9--16 9--19
#> + ... omitted several edges