There are two steps to using the fastRG package. First,
you must parameterize a random dot product graph by
sampling the latent factors. Use functions such as
dcsbm(), sbm(), etc, to perform this specification.
Then, use sample_*() functions to generate a random graph
in your preferred format.
Usage
sample_sparse(factor_model, ...)
# S3 method for undirected_factor_model
sample_sparse(factor_model, ...)
# S3 method for directed_factor_model
sample_sparse(factor_model, ...)Value
For undirected factor models, a sparse
Matrix::Matrix() of class dsCMatrix. In particular,
this means the Matrix object (1) has
double data type, (2) is symmetric, and (3) is in
column compressed storage format.
For directed factor models, a sparse
Matrix::Matrix() of class dgCMatrix. This means
the Matrix object (1) has double data type,
(2) in not symmetric, and (3) is in column
compressed storage format.
To reiterate: for undirected graphs, you will get a symmetric matrix. For directed graphs, you will get a general sparse matrix.
Details
This function implements the fastRG algorithm as
described in Rohe et al (2017). Please see the paper
(which is short and open access!!) for details.
References
Rohe, Karl, Jun Tao, Xintian Han, and Norbert Binkiewicz. 2017. "A Note on Quickly Sampling a Sparse Matrix with Low Rank Expectation." Journal of Machine Learning Research; 19(77):1-13, 2018. https://www.jmlr.org/papers/v19/17-128.html
See also
Other samplers:
sample_edgelist.matrix(),
sample_edgelist(),
sample_igraph(),
sample_tidygraph()
Examples
library(igraph)
library(tidygraph)
set.seed(27)
##### undirected examples ----------------------------
n <- 100
k <- 5
X <- matrix(rpois(n = n * k, 1), nrow = n)
S <- matrix(runif(n = k * k, 0, .1), nrow = k)
# S will be symmetrized internal here, or left unchanged if
# it is already symmetric
ufm <- undirected_factor_model(
X, S,
expected_density = 0.1
)
ufm
#> Undirected Factor Model
#> -----------------------
#>
#> Nodes (n): 100
#> Rank (k): 5
#>
#> X: 100 x 5 [dgeMatrix]
#> S: 5 x 5 [dgeMatrix]
#>
#> Poisson edges: TRUE
#> Allow self loops: TRUE
#>
#> Expected edges: 495
#> Expected degree: 5
#> Expected density: 0.1
### sampling graphs as edgelists ----------------------
edgelist <- sample_edgelist(ufm)
edgelist
#> # A tibble: 500 × 2
#> from to
#> <int> <int>
#> 1 66 71
#> 2 85 87
#> 3 37 54
#> 4 70 92
#> 5 14 44
#> 6 66 85
#> 7 76 83
#> 8 57 87
#> 9 57 95
#> 10 22 94
#> # … with 490 more rows
### sampling graphs as sparse matrices ----------------
A <- sample_sparse(ufm)
inherits(A, "dsCMatrix")
#> [1] TRUE
isSymmetric(A)
#> [1] TRUE
dim(A)
#> [1] 100 100
B <- sample_sparse(ufm)
inherits(B, "dsCMatrix")
#> [1] TRUE
isSymmetric(B)
#> [1] TRUE
dim(B)
#> [1] 100 100
### sampling graphs as igraph graphs ------------------
sample_igraph(ufm)
#> IGRAPH 5fe2ccb UN-- 100 486 --
#> + attr: name (v/c)
#> + edges from 5fe2ccb (vertex names):
#> [1] 65--87 84--100 12--87 13--95 3 --92 25--94 54--98 16--22 1 --66
#> [10] 13--94 65--79 12--66 79--94 55--56 30--64 13--22 22--40 37--80
#> [19] 88--95 22--11 85--94 52--94 37--11 12--16 19--75 47--74 63--97
#> [28] 12--61 11--73 2 --71 25--28 61--70 88--98 44--71 61--97 46--56
#> [37] 85--14 65--36 14--17 20--71 12--12 85--57 59--71 46--90 30--38
#> [46] 55--17 59--98 47--15 37--62 85--49 65--98 37--98 22--33 56--77
#> [55] 25--51 20--80 16--57 25--71 52--64 12--47 8 --80 79--18 22--62
#> [64] 14--31 37--69 54--16 26--90 38--94 79--20 70--97 19--90 11--71
#> + ... omitted several edges
### sampling graphs as tidygraph graphs ---------------
sample_tidygraph(ufm)
#> # A tbl_graph: 100 nodes and 501 edges
#> #
#> # An undirected multigraph with 1 component
#> #
#> # Node Data: 100 × 1 (active)
#> name
#> <int>
#> 1 1
#> 2 2
#> 3 3
#> 4 4
#> 5 5
#> 6 6
#> # … with 94 more rows
#> #
#> # Edge Data: 501 × 2
#> from to
#> <int> <int>
#> 1 54 94
#> 2 56 94
#> 3 16 22
#> # … with 498 more rows
##### directed examples ----------------------------
n2 <- 100
k1 <- 5
k2 <- 3
d <- 50
X <- matrix(rpois(n = n2 * k1, 1), nrow = n2)
S <- matrix(runif(n = k1 * k2, 0, .1), nrow = k1, ncol = k2)
Y <- matrix(rexp(n = k2 * d, 1), nrow = d)
fm <- directed_factor_model(X, S, Y, expected_in_degree = 2)
fm
#> Directed Factor Model
#> ---------------------
#>
#> Incoming Nodes (n): 100
#> Incoming Rank (k1): 5
#> Outgoing Rank (k2): 3
#> Outgoing Nodes (d): 50
#>
#> X: 100 x 5 [dgeMatrix]
#> S: 5 x 3 [dgeMatrix]
#> Y: 50 x 3 [dgeMatrix]
#>
#> Poisson edges: TRUE
#> Allow self loops: TRUE
#>
#> Expected edges: 100
#> Expected density: 0.02
#> Expected in degree: 2
#> Expected out degree: 1
### sampling graphs as edgelists ----------------------
edgelist2 <- sample_edgelist(fm)
edgelist2
#> # A tibble: 105 × 2
#> from to
#> <int> <int>
#> 1 84 34
#> 2 80 16
#> 3 42 30
#> 4 42 31
#> 5 47 26
#> 6 7 31
#> 7 39 14
#> 8 14 11
#> 9 49 47
#> 10 54 28
#> # … with 95 more rows
### sampling graphs as sparse matrices ----------------
A2 <- sample_sparse(fm)
inherits(A2, "dgCMatrix")
#> [1] TRUE
isSymmetric(A2)
#> [1] FALSE
dim(A2)
#> [1] 100 50
B2 <- sample_sparse(fm)
inherits(B2, "dgCMatrix")
#> [1] TRUE
isSymmetric(B2)
#> [1] FALSE
dim(B2)
#> [1] 100 50
### sampling graphs as igraph graphs ------------------
# since the number of rows and the number of columns
# in `fm` differ, we will get a bipartite igraph here
# creating the bipartite igraph is slow relative to other
# sampling -- if this is a blocker for
# you please open an issue and we can investigate speedups
dig <- sample_igraph(fm)
is_bipartite(dig)
#> [1] TRUE
### sampling graphs as tidygraph graphs ---------------
sample_tidygraph(fm)
#> # A tbl_graph: 150 nodes and 105 edges
#> #
#> # A bipartite multigraph with 59 components
#> #
#> # Node Data: 150 × 1 (active)
#> type
#> <lgl>
#> 1 FALSE
#> 2 FALSE
#> 3 FALSE
#> 4 FALSE
#> 5 FALSE
#> 6 FALSE
#> # … with 144 more rows
#> #
#> # Edge Data: 105 × 2
#> from to
#> <int> <int>
#> 1 55 101
#> 2 61 101
#> 3 89 101
#> # … with 102 more rows