Sample a random dot product graph as a sparse Matrix

Description

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 class 'undirected_factor_model'
sample_sparse(factor_model, ...)

## S3 method for class 'directed_factor_model'
sample_sparse(factor_model, ...)

Arguments

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.

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.

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

### sampling graphs as edgelists ----------------------

edgelist <- sample_edgelist(ufm)
edgelist

### sampling graphs as sparse matrices ----------------

A <- sample_sparse(ufm)

inherits(A, "dsCMatrix")
isSymmetric(A)
dim(A)

B <- sample_sparse(ufm)

inherits(B, "dsCMatrix")
isSymmetric(B)
dim(B)

### sampling graphs as igraph graphs ------------------

sample_igraph(ufm)

### sampling graphs as tidygraph graphs ---------------

sample_tidygraph(ufm)

##### 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

### sampling graphs as edgelists ----------------------

edgelist2 <- sample_edgelist(fm)
edgelist2

### sampling graphs as sparse matrices ----------------

A2 <- sample_sparse(fm)

inherits(A2, "dgCMatrix")
isSymmetric(A2)
dim(A2)

B2 <- sample_sparse(fm)

inherits(B2, "dgCMatrix")
isSymmetric(B2)
dim(B2)

### 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)

### sampling graphs as tidygraph graphs ---------------

sample_tidygraph(fm)