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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 f7c3843 U--- 10 31 -- 
#> + edges from f7c3843:
#>  [1] 1-- 4 1-- 5 1-- 6 1-- 7 1-- 8 1-- 9 1--10 2-- 4 2-- 5 2-- 6 2-- 8 2--10
#> [13] 3-- 4 3-- 5 3-- 8 3-- 9 3--10 4-- 5 4-- 7 4-- 8 4--10 5-- 6 5-- 7 5-- 8
#> [25] 6-- 7 6-- 8 7-- 8 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 2974242 U--- 20 128 -- 
#> + edges from 2974242:
#>  [1]  1-- 3  1-- 5  1-- 7  1-- 8  1-- 9  1--10  1--11  1--12  1--15  1--19
#> [11]  2-- 3  2-- 4  2-- 5  2-- 6  2-- 9  2--10  2--11  2--12  2--13  2--17
#> [21]  2--18  2--19  2--20  3-- 6  3-- 7  3-- 8  3-- 9  3--10  3--11  3--12
#> [31]  3--13  3--14  3--15  3--16  3--17  3--18  3--20  4-- 6  4--10  4--11
#> [41]  4--12  4--13  4--14  4--17  4--18  4--19  4--20  5-- 6  5-- 7  5--13
#> [51]  5--14  6-- 7  6-- 8  6-- 9  6--10  6--11  6--12  6--13  6--14  6--15
#> [61]  6--16  6--17  6--18  6--19  7-- 8  7--10  7--11  7--12  7--14  7--15
#> [71]  7--18  7--19  8-- 9  8--10  8--11  8--12  8--14  8--15  8--16  8--17
#> [81]  9--10  9--11  9--13  9--14  9--15  9--16  9--17  9--18 10--11 10--12
#> + ... omitted several edges