sample_edgelist: Sample a random edgelist from a random dot product graph

In fastRG: Sample Generalized Random Dot Product Graphs in Linear Time

Sample a random edgelist from a random dot product graph

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_edgelist(factor_model, ...)

## S3 method for class 'undirected_factor_model'
sample_edgelist(factor_model, ...)

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

Arguments

factor_model	A directed_factor_model() or undirected_factor_model().
...	Ignored. Do not use.

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

A single realization of a random Poisson (or Bernoulli) Dot Product Graph, represented as a tibble::tibble() with two integer columns, from and to.

NOTE: Indices for isolated nodes will not appear in the edgelist! This can lead to issues if you construct network objects from the edgelist directly.

In the undirected case, from and to do not encode information about edge direction, but we will always have from <= to for convenience of edge identification.

To avoid handling such considerations yourself, we recommend using sample_sparse(), sample_igraph(), and sample_tidygraph() over sample_edgelist().

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_igraph(), sample_sparse(), 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)

fastRG documentation built on Aug. 22, 2023, 1:08 a.m.