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Title:	Sample Generalized Random Dot Product Graphs in Linear Time
Version:	0.4.0
Description:	Samples generalized random product graphs, a generalization of a broad class of network models. Given matrices X, S, and Y with with non-negative entries, samples a matrix with expectation X S Y^T and independent Poisson or Bernoulli entries using the fastRG algorithm of Rohe et al. (2017)https://www.jmlr.org/papers/v19/17-128.html. The algorithm first samples the number of edges and then puts them down one-by-one. As a result it is O(m) where m is the number of edges, a dramatic improvement over element-wise algorithms that which require O(n^2) operations to sample a random graph, where n is the number of nodes.
License:	MIT + file LICENSE
URL:	https://rohelab.github.io/fastRG/,https://github.com/RoheLab/fastRG
BugReports:	https://github.com/RoheLab/fastRG/issues
Depends:	Matrix
Imports:	dplyr, ggplot2, glue, igraph, methods, rlang (≥ 1.0.0),RSpectra, stats, tibble, tidygraph, tidyr
Suggests:	covr, irlba, knitr, magrittr, purrr, rmarkdown, scales,testthat (≥ 3.0.0)
Config/testthat/edition:	3
Encoding:	UTF-8
RoxygenNote:	7.3.2
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2025-12-05 20:20:25 UTC; alex
Author:	Alex Hayes [aut, cre, cph], Karl Rohe [aut, cph], Jun Tao [aut], Xintian Han [aut], Norbert Binkiewicz [aut]
Maintainer:	Alex Hayes <alexpghayes@gmail.com>
Repository:	CRAN
Date/Publication:	2025-12-06 15:20:02 UTC

Create an undirected Chung-Lu object

Description

To specify a Chung-Lu graph, you must specifythe degree-heterogeneity parameters (vian ortheta).We provide reasonable defaults to enable rapid explorationor you can invest the effortfor more control over the model parameters. Westrongly recommendsetting theexpected_degree orexpected_density argumentto avoid large memory allocations associated withsampling large, dense graphs.

Usage

chung_lu(  n = NULL,  theta = NULL,  ...,  sort_nodes = TRUE,  poisson_edges = TRUE,  allow_self_loops = TRUE,  force_identifiability = FALSE)

Arguments

Value

Anundirected_chung_lu S3 object, a subclass ofdcsbm().

See Also

Other undirected graphs:dcsbm(),erdos_renyi(),mmsbm(),overlapping_sbm(),planted_partition(),sbm()

Examples

set.seed(27)cl <- chung_lu(n = 100, expected_density = 0.01)cltheta <- round(stats::rlnorm(100, 2))cl2 <- chung_lu(  theta = theta,  expected_degree = 5)cl2edgelist <- sample_edgelist(cl)edgelist

Create an undirected degree corrected stochastic blockmodel object

Description

To specify a degree-corrected stochastic blockmodel, you must specifythe degree-heterogeneity parameters (vian ortheta),the mixing matrix (viak orB), and the relative blockprobabilities (optional, viapi). We provide defaults for most of theseoptions to enable rapid exploration, or you can invest the effortfor more control over the model parameters. Westrongly recommendsetting theexpected_degree orexpected_density argumentto avoid large memory allocations associated withsampling large, dense graphs.

Usage

dcsbm(  n = NULL,  theta = NULL,  k = NULL,  B = NULL,  ...,  block_sizes = NULL,  pi = NULL,  sort_nodes = TRUE,  force_identifiability = FALSE,  poisson_edges = TRUE,  allow_self_loops = TRUE)

Arguments

Value

Anundirected_dcsbm S3 object, a subclass of theundirected_factor_model() with the following additionalfields:

• theta: A numeric vector of degree-heterogeneity parameters.

• z: The community memberships of each node, as afactor().The factor will havek levels, wherek is the number ofcommunities in the stochastic blockmodel. There will notalways necessarily be observed nodes in each community.

• pi: Sampling probabilities for each block.

• sorted: Logical indicating where nodes are arranged byblock (and additionally by degree heterogeneity parameter)within each block.

Generative Model

There are two levels of randomness in a degree-correctedstochastic blockmodel. First, we randomly chose a blockmembership for each node in the blockmodel. This ishandled bydcsbm(). Then, given these block memberships,we randomly sample edges between nodes. This secondoperation is handled bysample_edgelist(),sample_sparse(),sample_igraph() andsample_tidygraph(), depending depending on your desiredgraph representation.

Block memberships

Letz_i represent the block membership of nodei.To generatez_i we sample from a categoricaldistribution (note that this is a special case of amultinomial) with parameter\pi, such that\pi_i represents the probability of ending up inthe ith block. Block memberships for each node are independent.

Degree heterogeneity

In addition to block membership, the DCSBM also allowsnodes to have different propensities for edge formation.We represent this propensity for nodei by a positivenumber\theta_i. Typically the\theta_i areconstrained to sum to one for identifiability purposes,but this doesn't really matter during sampling (i.e.without the sum constraint scalingB and\thetahas the same effect on edge probabilities, but whetherB or\theta is responsible for this changeis uncertain).

Edge formulation

Once we know the block membershipsz and the degreeheterogeneity parameterstheta, we need one moreingredient, which is the baseline intensity of connectionsbetween nodes in blocki and blockj. Then each edgeA_{i,j} is Poisson distributed with parameter

\lambda[i, j] = \theta_i \cdot B_{z_i, z_j} \cdot \theta_j.

See Also

Other stochastic block models:directed_dcsbm(),mmsbm(),overlapping_sbm(),planted_partition(),sbm()

Other undirected graphs:chung_lu(),erdos_renyi(),mmsbm(),overlapping_sbm(),planted_partition(),sbm()

Examples

set.seed(27)lazy_dcsbm <- dcsbm(n = 100, k = 5, expected_density = 0.01)lazy_dcsbm# sometimes you gotta let the world burn and# sample a wildly dense graphdense_lazy_dcsbm <- dcsbm(n = 50, k = 3, expected_density = 0.8)dense_lazy_dcsbm# explicitly setting the degree heterogeneity parameter,# mixing matrix, and relative community sizes rather# than using randomly generated defaultsk <- 5n <- 100B <- matrix(stats::runif(k * k), nrow = k, ncol = k)theta <- round(stats::rlnorm(n, 2))pi <- c(1, 2, 4, 1, 1)custom_dcsbm <- dcsbm(  theta = theta,  B = B,  pi = pi,  expected_degree = 50)custom_dcsbmedgelist <- sample_edgelist(custom_dcsbm)edgelistdcsbm_explicit_block_sizes <- dcsbm(  theta = rexp(100, 1 / 3) + 1,  B = B,  block_sizes = c(13, 17, 40, 14, 16),  expected_degree = 5)# respects block sizessummary(dcsbm_explicit_block_sizes$z)# efficient eigendecompostion that leverages low-rank structure in# E(A) so that you don't have to form E(A) to find eigenvectors,# as E(A) is typically dense. computation is# handled via RSpectrapopulation_eigs <- eigs_sym(custom_dcsbm)

Create a directed degree corrected stochastic blockmodel object

Description

To specify a degree-corrected stochastic blockmodel, you must specifythe degree-heterogeneity parameters (vian ortheta_out andtheta_in), the mixing matrix(viak_out andk_in, orB), and the relative blockprobabilities (optional, viap_out andpi_in).We provide defaults for most of theseoptions to enable rapid exploration, or you can invest the effortfor more control over the model parameters. Westrongly recommendsetting theexpected_out_degree,expected_in_degree,orexpected_density argumentto avoid large memory allocations associated withsampling large, dense graphs.

Usage

directed_dcsbm(  n = NULL,  theta_out = NULL,  theta_in = NULL,  k_out = NULL,  k_in = NULL,  B = NULL,  ...,  pi_out = rep(1/k_out, k_out),  pi_in = rep(1/k_in, k_in),  sort_nodes = TRUE,  force_identifiability = TRUE,  poisson_edges = TRUE,  allow_self_loops = TRUE)

Arguments

Value

Adirected_dcsbm S3 object, a subclass of thedirected_factor_model() with the following additionalfields:

• theta_out: A numeric vector of incoming communitydegree-heterogeneity parameters.

• theta_in: A numeric vector of outgoing communitydegree-heterogeneity parameters.

• z_out: The incoming community memberships of each node,as afactor(). The factor will havek_out levels,wherek_out is the number of incomingcommunities in the stochastic blockmodel. There will notalways necessarily be observed nodes in each community.

• z_in: The outgoing community memberships of each node,as afactor(). The factor will havek_in levels,wherek_in is the number of outgoingcommunities in the stochastic blockmodel. There will notalways necessarily be observed nodes in each community.

• pi_out: Sampling probabilities for each incomingcommunity.

• pi_in: Sampling probabilities for each outgoingcommunity.

• sorted: Logical indicating where nodes are arranged byblock (and additionally by degree heterogeneity parameter)within each block.

Generative Model

There are two levels of randomness in a directed degree-correctedstochastic blockmodel. First, we randomly chose a incomingblock membership and an outgoing block membershipfor each node in the blockmodel. This ishandled bydirected_dcsbm(). Then, given these block memberships,we randomly sample edges between nodes. This secondoperation is handled bysample_edgelist(),sample_sparse(),sample_igraph() andsample_tidygraph(), depending on your desiredgraph representation.

Block memberships

Letx represent the incoming block membership of a nodeandy represent the outgoing block membership of a node.To generatex we sample from a categoricaldistribution with parameter\pi_out.To generatey we sample from a categoricaldistribution with parameter\pi_in.Block memberships are independent across nodes. Incoming and outgoingblock memberships of the same node are also independent.

Degree heterogeneity

In addition to block membership, the DCSBM alsonodes to have different propensities for incoming andoutgoing edge formation.We represent the propensity to form incoming edges for agiven node by a positive number\theta_out.We represent the propensity to form outgoing edges for agiven node by a positive number\theta_in.Typically the\theta_out (andtheta_in) across all nodes areconstrained to sum to one for identifiability purposes,but this doesn't really matter during sampling.

Edge formulation

Once we know the block membershipsx andyand the degree heterogeneity parameters\theta_{in} and\theta_{out}, we need one moreingredient, which is the baseline intensity of connectionsbetween nodes in blocki and blockj. Then each edge formsindependently according to a Poisson distribution withparameters

\lambda = \theta_{in} * B_{x, y} * \theta_{out}.

See Also

Other stochastic block models:dcsbm(),mmsbm(),overlapping_sbm(),planted_partition(),sbm()

Other directed graphs:directed_erdos_renyi()

Examples

set.seed(27)B <- matrix(0.2, nrow = 5, ncol = 8)diag(B) <- 0.9ddcsbm <- directed_dcsbm(  n = 100,  B = B,  k_out = 5,  k_in = 8,  expected_density = 0.01)ddcsbmpopulation_svd <- svds(ddcsbm)

Create an directed erdos renyi object

Description

Create an directed erdos renyi object

Usage

directed_erdos_renyi(  n,  ...,  p = NULL,  poisson_edges = TRUE,  allow_self_loops = TRUE)

Arguments

Value

Adirected_factor_model S3 class based on a listwith the following elements:

• X: The incoming latent positions as aMatrix::Matrix() object.

• S: The mixing matrix as aMatrix::Matrix() object.

• Y: The outgoing latent positions as aMatrix::Matrix() object.

• n: The number of nodes with incoming edges in the network.

• k1: The dimension of the latent node position vectorsencoding incoming latent communities (i.e. inX).

• d: The number of nodes with outgoing edges in the network.Does not need to matchn – rectangular adjacency matricesare supported.

• k2: The dimension of the latent node position vectorsencoding outgoing latent communities (i.e. inY).

• poisson_edges: Whether or not the graph is taken to be havePoisson or Bernoulli edges, as indicated by a logical vectorof length 1.

• allow_self_loops: Whether or not self loops are allowed.

See Also

Other erdos renyi:erdos_renyi()

Other directed graphs:directed_dcsbm()

Examples

set.seed(87)er <- directed_erdos_renyi(n = 10, p = 0.1)erbig_er <- directed_erdos_renyi(n = 1000, expected_in_degree = 5)big_erA <- sample_sparse(er)A

Create a directed factor model graph

Description

A directed factor model graph is a directedgeneralized Poisson random dot product graph. The edgesin this graph are assumpted to be independent and Poissondistributed. The graph is parameterized by its expectedadjacency matrix, with is⁠E[A] = X S Y'⁠. We do not recommendthat causal users use this function, see insteaddirected_dcsbm()and related functions, which will formulate common variantsof the stochastic blockmodels as undirected factor modelswith lots of helpful input validation.

Usage

directed_factor_model(  X,  S,  Y,  ...,  expected_in_degree = NULL,  expected_out_degree = NULL,  expected_density = NULL,  poisson_edges = TRUE,  allow_self_loops = TRUE)

Arguments

Value

Adirected_factor_model S3 class based on a listwith the following elements:

• X: The incoming latent positions as aMatrix::Matrix() object.

• S: The mixing matrix as aMatrix::Matrix() object.

• Y: The outgoing latent positions as aMatrix::Matrix() object.

• n: The number of nodes with incoming edges in the network.

• k1: The dimension of the latent node position vectorsencoding incoming latent communities (i.e. inX).

• d: The number of nodes with outgoing edges in the network.Does not need to matchn – rectangular adjacency matricesare supported.

• k2: The dimension of the latent node position vectorsencoding outgoing latent communities (i.e. inY).

• poisson_edges: Whether or not the graph is taken to be havePoisson or Bernoulli edges, as indicated by a logical vectorof length 1.

• allow_self_loops: Whether or not self loops are allowed.

Examples

n <- 1000k1 <- 5k2 <- 3d <- 500X <- matrix(rpois(n = n * k1, 1), nrow = n)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)fmfm2 <- directed_factor_model(X, S, Y, expected_in_degree = 50)fm2

Compute the eigendecomposition of the expected adjacency matrix of an undirected factor model

Description

Compute the eigendecomposition of the expected adjacency matrix of an undirected factor model

Usage

## S3 method for class 'undirected_factor_model'eigs_sym(A, k = A$k, which = "LM", sigma = NULL, opts = list(), ...)

Arguments

Details

Thewhich argument is a character stringthat specifies the type of eigenvalues to be computed.Possible values are:

eigs() with matrix types "matrix", "dgeMatrix", "dgCMatrix"and "dgRMatrix" can use "LM", "SM", "LR", "SR", "LI" and "SI".

eigs_sym() with all supported matrix types,andeigs() with symmetric matrix types("dsyMatrix", "dsCMatrix", and "dsRMatrix") can use "LM", "SM", "LA", "SA" and "BE".

Theopts argument is a list that can supply any of thefollowing parameters:

ncv

Number of Lanzcos basis vectors to use. More vectorswill result in faster convergence, but with greatermemory use. For general matrix,ncv must satisfyk+2\le ncv \le n, andfor symmetric matrix, the constraint isk < ncv \le n.Default ismin(n, max(2*k+1, 20)).

tol

Precision parameter. Default is 1e-10.

maxitr

Maximum number of iterations. Default is 1000.

retvec

Whether to compute eigenvectors. If FALSE,only calculate and return eigenvalues.

initvec

Initial vector of lengthn supplied to theArnoldi/Lanczos iteration. It may speed up the convergenceifinitvec is close to an eigenvector ofA.

Create an undirected erdos renyi object

Description

Create an undirected erdos renyi object

Usage

erdos_renyi(n, ..., p = NULL, poisson_edges = TRUE, allow_self_loops = TRUE)

Arguments

Value

Anundirected_factor_model S3 class based on a listwith the following elements:

• X: The latent positions as aMatrix::Matrix() object.

• S: The mixing matrix as aMatrix::Matrix() object.

• n: The number of nodes in the network.

• k: The rank of expectation matrix. Equivalently,the dimension of the latent node position vectors.

See Also

Other erdos renyi:directed_erdos_renyi()

Other undirected graphs:chung_lu(),dcsbm(),mmsbm(),overlapping_sbm(),planted_partition(),sbm()

Examples

set.seed(87)er <- erdos_renyi(n = 10, p = 0.1)erer <- erdos_renyi(n = 10, expected_density = 0.1)erbig_er <- erdos_renyi(n = 1000, expected_degree = 5)big_erA <- sample_sparse(er)A

Calculate the expected adjacency matrix

Description

Calculate the expected adjacency matrix

Usage

expectation(model, ...)## S3 method for class 'undirected_factor_model'expectation(model, ...)## S3 method for class 'directed_factor_model'expectation(model, ...)

Arguments

Value

The expected value of the adjacency matrix, conditional on thelatent factorsX andY (if the model is directed).

Calculate the expected edges in Poisson RDPG graph

Description

These calculations are conditional on the latent factorsX andY.

Usage

expected_edges(factor_model, ...)expected_degrees(factor_model, ...)expected_degree(factor_model, ...)expected_in_degree(factor_model, ...)expected_out_degree(factor_model, ...)expected_density(factor_model, ...)

Arguments

Details

Note that the runtime of thefastRG algorithm is proportional tothe expected number of edges in the graph. Expected edge count will bean underestimate of expected number of edges for Bernoulligraphs. See the Rohe et al for details.

Value

Expected edge counts, or graph densities.

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

Examples

##### an undirected blockmodel examplen <- 100pop <- n / 2a <- .1b <- .05B <- matrix(c(a, b, b, a), nrow = 2)b_model <- sbm(n = n, B = B, poisson_edges = FALSE)b_modelA <- sample_sparse(b_model)# comparemean(rowSums(triu(A)))pop * a + pop * b # analytical average degree##### more generic examplesn <- 1000k <- 5X <- matrix(rpois(n = n * k, 1), nrow = n)S <- matrix(runif(n = k * k, 0, .1), nrow = k)ufm <- undirected_factor_model(X, S)expected_edges(ufm)expected_degree(ufm)eigs_sym(ufm)n <- 1000d <- 100k1 <- 5k2 <- 3X <- matrix(rpois(n = n * k1, 1), nrow = n)Y <- matrix(rpois(n = d * k2, 1), nrow = d)S <- matrix(runif(n = k1 * k2, 0, .1), nrow = k1)dfm <- directed_factor_model(X = X, S = S, Y = Y)expected_edges(dfm)expected_in_degree(dfm)expected_out_degree(dfm)svds(dfm)

Create an undirected degree-corrected mixed membership stochastic blockmodel object

Description

To specify a degree-corrected mixed membership stochastic blockmodel, you must specifythe degree-heterogeneity parameters (vian ortheta),the mixing matrix (viak orB), and the relative blockpropensities (optional, viaalpha). We provide defaults for most of theseoptions to enable rapid exploration, or you can invest the effortfor more control over the model parameters. Westrongly recommendsetting theexpected_degree orexpected_density argumentto avoid large memory allocations associated withsampling large, dense graphs.

Usage

mmsbm(  n = NULL,  theta = NULL,  k = NULL,  B = NULL,  ...,  alpha = rep(1, k),  sort_nodes = TRUE,  force_pure = TRUE,  poisson_edges = TRUE,  allow_self_loops = TRUE)

Arguments

Value

Anundirected_mmsbm S3 object, a subclass of theundirected_factor_model() with the following additionalfields:

• theta: A numeric vector of degree-heterogeneity parameters.

• Z: The community memberships of each node, amatrix() withk columns, whose row sums all equal one.

• alpha: Community membership proportion propensities.

• sorted: Logical indicating where nodes are arranged byblock (and additionally by degree heterogeneity parameter)within each block.

Generative Model

There are two levels of randomness in a degree-correctedstochastic blockmodel. First, we randomly choose how mucheach node belongs to each block in the blockmodel. Each nodeis one unit of block membership to distribute. This ishandled bymmsbm(). Then, given these block memberships,we randomly sample edges between nodes. This secondoperation is handled bysample_edgelist(),sample_sparse(),sample_igraph() andsample_tidygraph(), depending depending on your desiredgraph representation.

Block memberships

LetZ_i by a vector on thek dimensional simplexrepresenting the block memberships of nodei.To generatez_i we sample from a Dirichletdistribution with parameter vector\alpha.Block memberships for each node are independent.

Degree heterogeneity

In addition to block membership, the MMSBM also allowsnodes to have different propensities for edge formation.We represent this propensity for nodei by a positivenumber\theta_i.

Edge formulation

Once we know the block membership vectorz_i, z_j and the degreeheterogeneity parameters\theta, we need one moreingredient, which is the baseline intensity of connectionsbetween nodes in blocki and blockj. This is given by ak \times k matrixB. Then each edgeA_{i,j} is Poisson distributed with parameter

\lambda_{i, j} = \theta_i \cdot z_i^T B z_j \cdot \theta_j.

See Also

Other stochastic block models:dcsbm(),directed_dcsbm(),overlapping_sbm(),planted_partition(),sbm()

Other undirected graphs:chung_lu(),dcsbm(),erdos_renyi(),overlapping_sbm(),planted_partition(),sbm()

Examples

set.seed(27)lazy_mmsbm <- mmsbm(n = 100, k = 5, expected_density = 0.01)lazy_mmsbm# sometimes you gotta let the world burn and# sample a wildly dense graphdense_lazy_mmsbm <- mmsbm(n = 500, k = 3, expected_density = 0.8)dense_lazy_mmsbm# explicitly setting the degree heterogeneity parameter,# mixing matrix, and relative community sizes rather# than using randomly generated defaultsk <- 5n <- 100B <- matrix(stats::runif(k * k), nrow = k, ncol = k)theta <- round(stats::rlnorm(n, 2))alpha <- c(1, 2, 4, 1, 1)custom_mmsbm <- mmsbm(  theta = theta,  B = B,  alpha = alpha,  expected_degree = 50)custom_mmsbmedgelist <- sample_edgelist(custom_mmsbm)edgelist# efficient eigendecompostion that leverages low-rank structure in# E(A) so that you don't have to form E(A) to find eigenvectors,# as E(A) is typically dense. computation is# handled via RSpectrapopulation_eigs <- eigs_sym(custom_mmsbm)svds(custom_mmsbm)$d

Create an undirected overlapping degree corrected stochastic blockmodel object

Description

To specify a overlapping stochastic blockmodel, you must specifythe number of nodes (vian),the mixing matrix (viak orB), and the blockprobabilities (optional, viapi). We provide defaults for most of theseoptions to enable rapid exploration, or you can invest the effortfor more control over the model parameters. Westrongly recommendsetting theexpected_degree orexpected_density argumentto avoid large memory allocations associated withsampling large, dense graphs.

Usage

overlapping_sbm(  n,  k = NULL,  B = NULL,  ...,  pi = rep(1/k, k),  sort_nodes = TRUE,  force_pure = TRUE,  poisson_edges = TRUE,  allow_self_loops = TRUE)

Arguments

Value

Anundirected_overlapping_sbm S3 object, a subclass of theundirected_factor_model() with the following additionalfields:

• pi: Sampling probabilities for each block.

• sorted: Logical indicating where nodes are arranged byblock (and additionally by degree heterogeneity parameter)within each block.

Generative Model

There are two levels of randomness in a degree-correctedoverlapping stochastic blockmodel. First, for each node, weindependently determine if that node is a member of each block. This ishandled byoverlapping_sbm(). Then, given these block memberships,we randomly sample edges between nodes. This secondoperation is handled bysample_edgelist(),sample_sparse(),sample_igraph() andsample_tidygraph(), depending depending on your desiredgraph representation.

Identifiability

In order to be identifiable, an overlapping SBM must satisfy two conditions:

1. B must be invertible, and

2. the must be at least one "pure node" in each block that belongs to noother blocks.

Block memberships

Note that some nodes may not belong to any blocks.

TODO

Edge formulation

Once we know the block memberships, we need one moreingredient, which is the baseline intensity of connectionsbetween nodes in blocki and blockj. Then each edgeA_{i,j} is Poisson distributed with parameter

TODO

References

Kaufmann, Emilie, Thomas Bonald, and Marc Lelarge."A Spectral Algorithm with Additive Clustering for the Recovery ofOverlapping Communities in Networks," Vol. 9925.Lecture Notes in Computer Science.Cham: Springer International Publishing, 2016.https://doi.org/10.1007/978-3-319-46379-7.

Latouche, Pierre, Etienne Birmelé, and Christophe Ambroise."Overlapping Stochastic Block Models with Application to theFrench Political Blogosphere." The Annals of Applied Statistics 5,no. 1 (March 2011): 309–36. https://doi.org/10.1214/10-AOAS382.

Zhang, Yuan, Elizaveta Levina, and Ji Zhu. "DetectingOverlapping Communities in Networks Using Spectral Methods."ArXiv:1412.3432, December 10, 2014. http://arxiv.org/abs/1412.3432.

See Also

Other stochastic block models:dcsbm(),directed_dcsbm(),mmsbm(),planted_partition(),sbm()

Other undirected graphs:chung_lu(),dcsbm(),erdos_renyi(),mmsbm(),planted_partition(),sbm()

Examples

set.seed(27)lazy_overlapping_sbm <- overlapping_sbm(n = 1000, k = 5, expected_density = 0.01)lazy_overlapping_sbm# sometimes you gotta let the world burn and# sample a wildly dense graphdense_lazy_overlapping_sbm <- overlapping_sbm(n = 500, k = 3, expected_density = 0.8)dense_lazy_overlapping_sbmk <- 5n <- 1000B <- matrix(stats::runif(k * k), nrow = k, ncol = k)pi <- c(1, 2, 4, 1, 1) / 5custom_overlapping_sbm <- overlapping_sbm(  n = 200,  B = B,  pi = pi,  expected_degree = 5)custom_overlapping_sbmedgelist <- sample_edgelist(custom_overlapping_sbm)edgelist# efficient eigendecompostion that leverages low-rank structure in# E(A) so that you don't have to form E(A) to find eigenvectors,# as E(A) is typically dense. computation is# handled via RSpectrapopulation_eigs <- eigs_sym(custom_overlapping_sbm)

Create an undirected planted partition object

Description

To specify a planted partition model, you must specifythe number of nodes (vian), the mixing matrix (optional, either viawithin_block/between_block ora/b),and the relative block probabilites (optional, viapi).We provide defaults for most of these options to enablerapid exploration, or you can invest the effortfor more control over the model parameters. Westrongly recommendsetting theexpected_degree orexpected_density argumentto avoid large memory allocations associated withsampling large, dense graphs.

Usage

planted_partition(  n,  k,  ...,  within_block = NULL,  between_block = NULL,  a = NULL,  b = NULL,  block_sizes = NULL,  pi = NULL,  sort_nodes = TRUE,  poisson_edges = TRUE,  allow_self_loops = TRUE)

Arguments

Details

A planted partition model is stochastic blockmodel in whichthe diagonal and the off-diagonal of the mixing matrixBare both constant. This means that edge probabilitiesdepend only on whether two nodes belong to the same block,or to different blocks, but the particular blocks themselvesdon't have any impact apart from this.

Value

Anundirected_planted_partition S3 object, which is a subclassof thesbm() object, with additional fields:

• within_block: The probability of edge formation within a block.

• between_block: The probability of edge formation between two distinctblocks.

See Also

Other stochastic block models:dcsbm(),directed_dcsbm(),mmsbm(),overlapping_sbm(),sbm()

Other undirected graphs:chung_lu(),dcsbm(),erdos_renyi(),mmsbm(),overlapping_sbm(),sbm()

Examples

set.seed(27)lazy_pp <- planted_partition(  n = 100,  k = 5,  expected_density = 0.01,  within_block = 0.1,  between_block = 0.01)lazy_pp

Plot (expected) adjacency matrices

Description

Plot (expected) adjacency matrices

Usage

plot_expectation(model)plot_dense_matrix(A, ...)plot_sparse_matrix(A)

Arguments

Value

Aggplot2::ggplot2() plot.

Examples

set.seed(27)model <- dcsbm(n = 10, k = 2, expected_density = 0.2)plot_expectation(model)A <- sample_sparse(model)plot_sparse_matrix(A)

Objects exported from other packages

Description

These objects are imported from other packages. Follow the linksbelow to see their documentation.

RSpectra

eigs_sym,svds

Sample a random edgelist from a random dot product graph

Description

There are two steps to using thefastRG package. First,you must parameterize a random dot product graph bysampling the latent factors. Use functions such asdcsbm(),sbm(), etc, to perform this specification.Then, use⁠sample_*()⁠ functions to generate a random graphin 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

Details

This function implements thefastRG algorithm asdescribed 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 atibble::tibble() with twointeger columns,from andto.

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

In the undirected case,from andto do not encodeinformation about edge direction, but we will always havefrom <= to for convenience of edge identification.

To avoid handling such considerations yourself, we recommend usingsample_sparse(),sample_igraph(), andsample_tidygraph()oversample_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 <- 100k <- 5X <- 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 symmetricufm <- 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 <- 100k1 <- 5k2 <- 3d <- 50X <- 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 speedupsdig <- sample_igraph(fm)is_bipartite(dig)### sampling graphs as tidygraph graphs ---------------sample_tidygraph(fm)

Low level interface to sample RPDG edgelists

Description

This is a brakes-off, no safety checks interface.We strongly recommend that you do not callsample_edgelist.matrix() unless you know what you are doing,and even then, we still do not recommend it, as you willbypass all typical input validation.extremely loud coughing All those who bypass inputvalidation suffer foolishly at their own hand.extremely loud coughing

Usage

## S3 method for class 'matrix'sample_edgelist(  factor_model,  S,  Y,  directed,  poisson_edges,  allow_self_loops,  ...)## S3 method for class 'Matrix'sample_edgelist(  factor_model,  S,  Y,  directed,  poisson_edges,  allow_self_loops,  ...)

Arguments

Details

This function implements thefastRG algorithm asdescribed 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 atibble::tibble() with twointeger columns,from andto.

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

In the undirected case,from andto do not encodeinformation about edge direction, but we will always havefrom <= to for convenience of edge identification.

To avoid handling such considerations yourself, we recommend usingsample_sparse(),sample_igraph(), andsample_tidygraph()oversample_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(),sample_igraph(),sample_sparse(),sample_tidygraph()

Examples

set.seed(46)n <- 10000d <- 1000k1 <- 5k2 <- 3X <- matrix(rpois(n = n * k1, 1), nrow = n)S <- matrix(runif(n = k1 * k2, 0, .1), nrow = k1)Y <- matrix(rpois(n = d * k2, 1), nrow = d)sample_edgelist(X, S, Y, TRUE, TRUE, TRUE)

Sample a random dot product graph as an igraph graph

Description

There are two steps to using thefastRG package. First,you must parameterize a random dot product graph bysampling the latent factors. Use functions such asdcsbm(),sbm(), etc, to perform this specification.Then, use⁠sample_*()⁠ functions to generate a random graphin your preferred format.

Usage

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

Arguments

Details

This function implements thefastRG algorithm asdescribed in Rohe et al (2017). Please see the paper(which is short and open access!!) for details.

Value

Anigraph::igraph() object that is possibly amultigraph (that is, we take there to be multiple edgesrather than weighted edges).

Whenfactor_model isundirected:

- the graph is undirected and one-mode.

Whenfactor_model isdirected andsquare:

- the graph is directed and one-mode.

Whenfactor_model isdirected andrectangular:

- the graph is undirected and bipartite.

Note that working with bipartite graphs inigraph is morecomplex than working with one-mode graphs.

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(),sample_edgelist.matrix(),sample_sparse(),sample_tidygraph()

Examples

library(igraph)library(tidygraph)set.seed(27)##### undirected examples ----------------------------n <- 100k <- 5X <- 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 symmetricufm <- 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 <- 100k1 <- 5k2 <- 3d <- 50X <- 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 speedupsdig <- sample_igraph(fm)is_bipartite(dig)### sampling graphs as tidygraph graphs ---------------sample_tidygraph(fm)

Sample a random dot product graph as a sparse Matrix

Description

There are two steps to using thefastRG package. First,you must parameterize a random dot product graph bysampling the latent factors. Use functions such asdcsbm(),sbm(), etc, to perform this specification.Then, use⁠sample_*()⁠ functions to generate a random graphin 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 thefastRG algorithm asdescribed in Rohe et al (2017). Please see the paper(which is short and open access!!) for details.

Value

For undirected factor models, a sparseMatrix::Matrix() of classdsCMatrix. In particular,this means theMatrix object (1) hasdouble data type, (2) is symmetric, and (3) is incolumn compressed storage format.

For directed factor models, a sparseMatrix::Matrix() of classdgCMatrix. This meanstheMatrix object (1) has double data type,(2) innot symmetric, and (3) is in columncompressed storage format.

To reiterate: for undirected graphs, you will geta symmetric matrix. For directed graphs, you willget 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(),sample_edgelist.matrix(),sample_igraph(),sample_tidygraph()

Examples

library(igraph)library(tidygraph)set.seed(27)##### undirected examples ----------------------------n <- 100k <- 5X <- 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 symmetricufm <- 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 <- 100k1 <- 5k2 <- 3d <- 50X <- 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 speedupsdig <- sample_igraph(fm)is_bipartite(dig)### sampling graphs as tidygraph graphs ---------------sample_tidygraph(fm)

Sample a random dot product graph as a tidygraph graph

Description

There are two steps to using thefastRG package. First,you must parameterize a random dot product graph bysampling the latent factors. Use functions such asdcsbm(),sbm(), etc, to perform this specification.Then, use⁠sample_*()⁠ functions to generate a random graphin your preferred format.

Usage

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

Arguments

Details

This function implements thefastRG algorithm asdescribed in Rohe et al (2017). Please see the paper(which is short and open access!!) for details.

Value

Atidygraph::tbl_graph() object that is possibly amultigraph (that is, we take there to be multiple edgesrather than weighted edges).

Whenfactor_model isundirected:

- the graph is undirected and one-mode.

Whenfactor_model isdirected andsquare:

- the graph is directed and one-mode.

Whenfactor_model isdirected andrectangular:

- the graph is undirected and bipartite.

Note that working with bipartite graphs intidygraph is morecomplex than working with one-mode graphs.

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(),sample_edgelist.matrix(),sample_igraph(),sample_sparse()

Examples

library(igraph)library(tidygraph)set.seed(27)##### undirected examples ----------------------------n <- 100k <- 5X <- 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 symmetricufm <- 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 <- 100k1 <- 5k2 <- 3d <- 50X <- 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 speedupsdig <- sample_igraph(fm)is_bipartite(dig)### sampling graphs as tidygraph graphs ---------------sample_tidygraph(fm)

Create an undirected stochastic blockmodel object

Description

To specify a stochastic blockmodel, you must specifythe number of nodes (vian), the mixing matrix (viak orB),and the relative block probabilites (optional, viapi).We provide defaults for most of these options to enablerapid exploration, or you can invest the effortfor more control over the model parameters. Westrongly recommendsetting theexpected_degree orexpected_density argumentto avoid large memory allocations associated withsampling large, dense graphs.

Usage

sbm(  n,  k = NULL,  B = NULL,  ...,  block_sizes = NULL,  pi = NULL,  sort_nodes = TRUE,  poisson_edges = TRUE,  allow_self_loops = TRUE)

Arguments

Details

A stochastic block is equivalent to a degree-correctedstochastic blockmodel where the degree heterogeneity parametershave all been set equal to 1.

Value

Anundirected_sbm S3 object, which is a subclass of thedcsbm() object.

See Also

Other stochastic block models:dcsbm(),directed_dcsbm(),mmsbm(),overlapping_sbm(),planted_partition()

Other undirected graphs:chung_lu(),dcsbm(),erdos_renyi(),mmsbm(),overlapping_sbm(),planted_partition()

Examples

set.seed(27)lazy_sbm <- sbm(n = 100, k = 5, expected_density = 0.01)lazy_sbm# by default we get a multigraph (i.e. multiple edges are# allowed between the same two nodes). using bernoulli edges# will with an adjacency matrix with only zeroes and onesbernoulli_sbm <- sbm(  n = 500,  k = 30,  poisson_edges = FALSE,  expected_degree = 8)bernoulli_sbmedgelist <- sample_edgelist(bernoulli_sbm)edgelistA <- sample_sparse(bernoulli_sbm)# only zeroes and ones!sign(A)# sbm with repeated eigenvalues# block sizes equal by default, needed to prevent variation in spectrum# from variation in block sizes. also need B to have a single repeated# eigenvaluerepeated_eigen <- sbm(  n = 100,  B = diag(rep(0.8, 5)),  expected_degree = 10)# exactly repeated eigenvalues in the populatione <- eigs_sym(repeated_eigen)e$values

Compute the singular value decomposition of the expected adjacency matrix of a directed factor model

Description

Compute the singular value decomposition of the expected adjacency matrix of a directed factor model

Usage

## S3 method for class 'directed_factor_model'svds(A, k = min(A$k1, A$k2), nu = k, nv = k, opts = list(), ...)

Arguments

Details

Theopts argument is a list that can supply any of thefollowing parameters:

ncv

Number of Lanzcos basis vectors to use. More vectorswill result in faster convergence, but with greatermemory use.ncv must be satisfyk < ncv \le p wherep = min(m, n).Default ismin(p, max(2*k+1, 20)).

tol

Precision parameter. Default is 1e-10.

maxitr

Maximum number of iterations. Default is 1000.

center

Either a logical value (TRUE/FALSE), or a numericvector of lengthn. If a vectorc is supplied, thenSVD is computed on the matrixA - 1c',in an implicit way without actually forming this matrix.center = TRUE has the same effect ascenter = colMeans(A). Default isFALSE.

scale

Either a logical value (TRUE/FALSE), or a numericvector of lengthn. If a vectors is supplied, thenSVD is computed on the matrix(A - 1c')S,wherec is the centering vector andS = diag(1/s).Ifscale = TRUE, then the vectors is computed asthe column norm ofA - 1c'.Default isFALSE.

Compute the singular value decomposition of the expected adjacency matrix of an undirected factor model

Description

Compute the singular value decomposition of the expected adjacency matrix of an undirected factor model

Usage

## S3 method for class 'undirected_factor_model'svds(A, k = A$k, nu = k, nv = k, opts = list(), ...)

Arguments

Details

Theopts argument is a list that can supply any of thefollowing parameters:

ncv

Number of Lanzcos basis vectors to use. More vectorswill result in faster convergence, but with greatermemory use.ncv must be satisfyk < ncv \le p wherep = min(m, n).Default ismin(p, max(2*k+1, 20)).

tol

Precision parameter. Default is 1e-10.

maxitr

Maximum number of iterations. Default is 1000.

center

Either a logical value (TRUE/FALSE), or a numericvector of lengthn. If a vectorc is supplied, thenSVD is computed on the matrixA - 1c',in an implicit way without actually forming this matrix.center = TRUE has the same effect ascenter = colMeans(A). Default isFALSE.

scale

Either a logical value (TRUE/FALSE), or a numericvector of lengthn. If a vectors is supplied, thenSVD is computed on the matrix(A - 1c')S,wherec is the centering vector andS = diag(1/s).Ifscale = TRUE, then the vectors is computed asthe column norm ofA - 1c'.Default isFALSE.

Create an undirected factor model graph

Description

An undirected factor model graph is an undirectedgeneralized Poisson random dot product graph. The edgesin this graph are assumed to be independent and Poissondistributed. The graph is parameterized by its expectedadjacency matrix, which is⁠E[A|X] = X S X'⁠. We do not recommendthat casual users use this function, see insteaddcsbm()and related functions, which will formulate common variantsof the stochastic blockmodels as undirected factor modelswith lots of helpful input validation.

Usage

undirected_factor_model(  X,  S,  ...,  expected_degree = NULL,  expected_density = NULL,  poisson_edges = TRUE,  allow_self_loops = TRUE)

Arguments

Value

Anundirected_factor_model S3 class based on a listwith the following elements:

• X: The latent positions as aMatrix::Matrix() object.

• S: The mixing matrix as aMatrix::Matrix() object.

• n: The number of nodes in the network.

• k: The rank of expectation matrix. Equivalently,the dimension of the latent node position vectors.

Examples

n <- 100k <- 5X <- matrix(rpois(n = n * k, 1), nrow = n)S <- matrix(runif(n = k * k, 0, .1), nrow = k)ufm <- undirected_factor_model(X, S)ufmufm2 <- undirected_factor_model(X, S, expected_degree = 50)ufm2svds(ufm2)