Title: Stochastic Blockmodels
Version: 0.4.7
Description: A collection of tools and functions to adjust a variety of stochastic blockmodels (SBM). Supports at the moment Simple, Bipartite, 'Multipartite' and Multiplex SBM (undirected or directed with Bernoulli, Poisson or Gaussian emission laws on the edges, and possibly covariate for Simple and Bipartite SBM). See Léger (2016) <doi:10.48550/arXiv.1602.07587>, 'Barbillon et al.' (2020) <doi:10.1111/rssa.12193> and 'Bar-Hen et al.' (2020) <doi:10.48550/arXiv.1807.10138>.
URL: https://grosssbm.github.io/sbm/
BugReports: https://github.com/GrossSBM/sbm/issues
License: GPL (≥ 3)
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.3.2
Suggests: testthat, spelling, knitr, rmarkdown, aricode, covr
Language: en-US
Imports: alluvial, magrittr, dplyr, purrr, blockmodels, R6, Rcpp, igraph, ggplot2, GREMLINS, stringr, rlang, reshape2, prodlim
Collate: 'R6Class-SBM.R' 'R6Class-BipartiteSBM.R' 'R6Class-BipartiteSBM_fit.R' 'R6Class-MultipartiteSBM.R' 'R6Class-MultipartiteSBM_fit.R' 'R6Class-MultiplexSBM_fit.R' 'R6Class-SimpleSBM.R' 'R6Class-SimpleSBM_fit.R' 'RcppExports.R' 'defineSBM.R' 'estimate.R' 'fungusTreeNetwork.R' 'multipartiteEcologicalNetwork.R' 'plotAlluvial.R' 'plotMyMatrix.R' 'plotMyMultipartiteMatrix.R' 'plotMyMultiplexMatrix.R' 'sample.R' 'sbm-package.R' 'utils-pipe.R' 'utils.R' 'utils_plot.R' 'war.R'
LinkingTo: Rcpp, RcppArmadillo
VignetteBuilder: knitr
Depends: R (≥ 3.5.0)
NeedsCompilation: yes
Packaged: 2024-09-16 15:34:55 UTC; jchiquet
Author: Julien Chiquet ORCID iD [aut, cre], Sophie Donnet ORCID iD [aut], großBM team [ctb], Pierre Barbillon ORCID iD [aut]
Maintainer: Julien Chiquet <julien.chiquet@inrae.fr>
Repository: CRAN
Date/Publication: 2024-09-16 18:40:09 UTC

sbm: Stochastic Blockmodels

Description

A collection of tools and functions to adjust a variety of stochastic blockmodels (SBM). Supports at the moment Simple, Bipartite, 'Multipartite' and Multiplex SBM (undirected or directed with Bernoulli, Poisson or Gaussian emission laws on the edges, and possibly covariate for Simple and Bipartite SBM). See Léger (2016) doi:10.48550/arXiv.1602.07587, 'Barbillon et al.' (2020) doi:10.1111/rssa.12193 and 'Bar-Hen et al.' (2020) doi:10.48550/arXiv.1807.10138.

Author(s)

Maintainer: Julien Chiquet julien.chiquet@inrae.fr (ORCID)

Authors:

Other contributors:

See Also

Useful links:

Pipe operator

Description

See magrittr::%>% for details.

Usage

lhs %>% rhs

R6 class for Bipartite SBM

Description

R6 class for Bipartite SBM

R6 class for Bipartite SBM

Super class

sbm::SBM -> BipartiteSBM

Active bindings

dimLabels

vector of two characters giving the label of each connected dimension (row, col)

blockProp

list of two vectors of block proportions (aka prior probabilities of each block)

connectParam

parameters associated to the connectivity of the SBM, e.g. matrix of inter/inter block probabilities when model is Bernoulli

probMemberships

matrix of estimated probabilities for block memberships for all nodes

nbBlocks

vector of size 2: number of blocks (rows, columns)

nbDyads

number of dyads (potential edges in the network)

nbConnectParam

number of parameter used for the connectivity

memberships

list of size 2: vector of memberships in row, in column.

indMemberships

matrix for clustering memberships

Methods

Public methods

Inherited methods

Method new()

constructor for SBM

Usage
BipartiteSBM$new(
  model,
  nbNodes,
  blockProp,
  connectParam,
  dimLabels = c(row = "row", col = "col"),
  covarParam = numeric(length(covarList)),
  covarList = list()
)
Arguments
model

character describing the type of model

nbNodes

number of nodes in each dimension of the network

blockProp

parameters for block proportions (vector of list of vectors)

connectParam

list of parameters for connectivity with a matrix of means 'mean' and an optional scalar for the variance 'var'. The dimensions of mu must match blockProp lengths

dimLabels

optional labels of each dimension (in row, in column)

covarParam

optional vector of covariates effect

covarList

optional list of covariates data

Method rMemberships()

a method to sample new block memberships for the current SBM

Usage
BipartiteSBM$rMemberships(store = FALSE)
Arguments
store

should the sampled blocks be stored (and overwrite the existing data)? Default to FALSE

Returns

the sampled blocks

Method rEdges()

a method to sample a network data (edges) for the current SBM

Usage
BipartiteSBM$rEdges(store = FALSE)
Arguments
store

should the sampled edges be stored (and overwrite the existing data)? Default to FALSE

Returns

the sampled network

Method predict()

prediction under the current parameters

Usage
BipartiteSBM$predict(covarList = self$covarList, theta_p0 = 0)
Arguments
covarList

a list of covariates. By default, we use the covariates with which the model was estimated.

theta_p0

double for thresholding...

Method show()

show method

Usage
BipartiteSBM$show(type = "Bipartite Stochastic Block Model")
Arguments
type

character used to specify the type of SBM

Method plot()

basic matrix plot method for BipartiteSBM object or mesoscopic plot

Usage
BipartiteSBM$plot(
  type = c("data", "expected", "meso"),
  ordered = TRUE,
  plotOptions = list()
)
Arguments
type

character for the type of plot: either 'data' (true connection), 'expected' (fitted connection) or 'meso' (mesoscopic view). Default to 'data'.

ordered

logical: should the rows and columns be reordered according to the clustering? Default to TRUE.

plotOptions

list with the parameters for the plot. See help of the corresponding S3 method for details.

Returns

a ggplot2 object for the 'data' and 'expected', a list with the igraph object g, the layout and the plotOptions for the 'meso'

Method clone()

The objects of this class are cloneable with this method.

Usage
BipartiteSBM$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

R6 Class definition of an Bipartite SBM fit

Description

R6 Class definition of an Bipartite SBM fit

R6 Class definition of an Bipartite SBM fit

Details

This class is designed to give a representation and adjust an LBM fitted with blockmodels.

Super classes

sbm::SBM -> sbm::BipartiteSBM -> BipartiteSBM_fit

Active bindings

loglik

double: approximation of the log-likelihood (variational lower bound) reached

ICL

double: value of the integrated classification log-likelihood

penalty

double, value of the penalty term in ICL

entropy

double, value of the entropy due to the clustering distribution

storedModels

data.frame of all models fitted (and stored) during the optimization

Methods

Public methods

Inherited methods

Method new()

constructor for a Bipartite SBM fit

Usage
BipartiteSBM_fit$new(
  incidenceMatrix,
  model,
  dimLabels = c(row = "row", col = "col"),
  covarList = list()
)
Arguments
incidenceMatrix

rectangular (weighted) matrix

model

character ('bernoulli', 'poisson', 'gaussian')

dimLabels

labels of each dimension (in row, in columns)

covarList

and optional list of covariates, each of whom must have the same dimension as incidenceMatrix

Method optimize()

function to perform optimization

Usage
BipartiteSBM_fit$optimize(estimOptions = list())
Arguments
estimOptions

a list of parameters controlling the inference algorithm and model selection. See details.

Method setModel()

method to select a specific model among the ones fitted during the optimization. Fields of the current SBM_fit will be updated accordingly.

Usage
BipartiteSBM_fit$setModel(index)
Arguments
index

integer, the index of the model to be selected (row number in storedModels)

Method reorder()

permute group labels by order of decreasing probability

Usage
BipartiteSBM_fit$reorder()

Method show()

show method

Usage
BipartiteSBM_fit$show(type = "Fit of a Bipartite Stochastic Block Model")
Arguments
type

character used to specify the type of SBM

Method clone()

The objects of this class are cloneable with this method.

Usage
BipartiteSBM_fit$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

R6 Class definition of a Multipartite SBM

Description

R6 Class definition of a Multipartite SBM

R6 Class definition of a Multipartite SBM

Super class

sbm::SBM -> MultipartiteSBM

Active bindings

dimLabels

vector of characters giving the label of each connected dimension

blockProp

list of two vectors of block proportions (aka prior probabilities of each block)

connectParam

parameters associated to the connectivity of the SBM, e.g. matrix of inter/inter block probabilities when model is Bernoulli

probMemberships

matrix of estimated probabilities for block memberships for all nodes

nbBlocks

: vector with the number of blocks in each FG

nbConnectParam

number of parameter used for the connectivity

architecture

organization of the multipartite network

nbNetworks

number of networks in the multipartite network

memberships

list of size 2: vector of memberships in all parts of the network

indMemberships

matrix for clustering memberships

Methods

Public methods

Inherited methods

Method new()

constructor for Multipartite SBM

Usage
MultipartiteSBM$new(
  model = character(0),
  architecture = matrix(NA, 0, 2),
  directed = logical(0),
  nbNodes = numeric(0),
  dimLabels = character(0),
  blockProp = list(),
  connectParam = list()
)
Arguments
model

character describing the type of model

architecture

a 2-column matrix describing interactions between the networks

directed

vector of logical: are the network directed or not?

nbNodes

number of nodes in each dimension/part of the network

dimLabels

labels of each par of the network

blockProp

parameters for block proportions (vector of list of vectors)

connectParam

parameters of connectivity (vector of list of vectors)

Method show()

print method

Usage
MultipartiteSBM$show(type = "Multipartite Stochastic Block Model")
Arguments
type

character to tune the displayed name

Method print()

print method

Usage
MultipartiteSBM$print()

Method plot()

plot Multipartite Network

Usage
MultipartiteSBM$plot(
  type = c("data", "expected", "meso"),
  ordered = TRUE,
  plotOptions = list()
)
Arguments
type

character for the type of plot: either 'data' (true connection), 'expected' (fitted connection) or 'meso' (mesoscopic view). Default to 'data'.

ordered

TRUE is the matrices are plotted after reorganization with the blocks. Default value = TRUE

plotOptions

list of plot options for the mesoscopic view or matrix view

Method clone()

The objects of this class are cloneable with this method.

Usage
MultipartiteSBM$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

R6 Class definition of a Multipartite SBM fit

Description

R6 Class definition of a Multipartite SBM fit

R6 Class definition of a Multipartite SBM fit

Details

This class is designed to give a representation and adjust a Multipartite SBM fitted with GREMLIN.

Super classes

sbm::SBM -> sbm::MultipartiteSBM -> MultipartiteSBM_fit

Active bindings

loglik

double: approximation of the log-likelihood (variational lower bound) reached

ICL

double: value of the integrated classification log-likelihood

storedModels

data.frame of all models fitted (and stored) during the optimization

Methods

Public methods

Inherited methods

Method new()

constructor for Multipartite SBM

Usage
MultipartiteSBM_fit$new(netList)
Arguments
netList

list of SBM objects

Method optimize()

estimation of multipartiteSBM via GREMLINS

Usage
MultipartiteSBM_fit$optimize(estimOptions)
Arguments
estimOptions

options for MultipartiteBM

Method predict()

prediction under the currently estimated model

Usage
MultipartiteSBM_fit$predict()
Returns

a list of matrices matrix of expected values for each dyad

Method setModel()

method to select a specific model among the ones fitted during the optimization. Fields of the current MultipartiteSBM_fit will be updated accordingly.

Usage
MultipartiteSBM_fit$setModel(index)
Arguments
index

integer, the index of the model to be selected (row number in storedModels)

Method show()

show method

Usage
MultipartiteSBM_fit$show(type = "Fit of a Multipartite Stochastic Block Model")
Arguments
type

character used to specify the type of SBM

Method clone()

The objects of this class are cloneable with this method.

Usage
MultipartiteSBM_fit$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

R6 Class definition of a Multiplex SBM fit

Description

R6 Class definition of a Multiplex SBM fit

R6 Class definition of a Multiplex SBM fit

Details

This class is designed to give a representation and adjust a Multiplex SBM fitted with GREMLIN.

The list of parameters estimOptions essentially tunes the optimization process and the variational EM algorithm, with the following parameters

Super classes

sbm::SBM -> sbm::MultipartiteSBM -> sbm::MultipartiteSBM_fit -> MultiplexSBM_fit

Active bindings

nbBlocks

vector of size 2: number of blocks (rows, columns)

dependentNetwork

: connection parameters in each network

storedModels

data.frame of all models fitted (and stored) during the optimization

namesLayers

: names of the various Networks

Methods

Public methods

Inherited methods

Method new()

constructor for Multiplex SBM

Usage
MultiplexSBM_fit$new(netList, dependentNet = FALSE)
Arguments
netList

list of SBM object with

dependentNet

boolean indicating whether dependence is assumed between networks beyond the common dependence on the latent variables

Method optimize()

estimation of multipartiteSBM via GREMLINS

Usage
MultiplexSBM_fit$optimize(estimOptions)
Arguments
estimOptions

options for MultipartiteBM

Method plot()

plot Multiplex Network

Usage
MultiplexSBM_fit$plot(
  type = c("data", "expected"),
  ordered = TRUE,
  plotOptions = list()
)
Arguments
type

character for the type of plot: either 'data' (true connection), 'expected' (fitted connection). Default to 'data'.

ordered

TRUE is the matrices are plotted after reorganization with the blocks. Default value = TRUE

plotOptions

list of plot options for the matrix view

Method show()

show method

Usage
MultiplexSBM_fit$show(type = "Fit of a Multiplex Stochastic Block Model")
Arguments
type

character used to specify the type of SBM

Method predict()

prediction under the currently estimated model

Usage
MultiplexSBM_fit$predict()
Returns

a list of matrices matrix of expected values for each dyad

Method clone()

The objects of this class are cloneable with this method.

Usage
MultiplexSBM_fit$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

R6 virtual class for SBM representation (mother class of SimpleSBM, BipartiteSBM, MultipartiteSBM)

Description

R6 virtual class for SBM representation (mother class of SimpleSBM, BipartiteSBM, MultipartiteSBM)

R6 virtual class for SBM representation (mother class of SimpleSBM, BipartiteSBM, MultipartiteSBM)

Active bindings

modelName

character, the family of model for the distribution of the edges

directed

mode of the network data (directed or not or not applicable)

dimLabels

vector or list of characters, the label of each dimension

nbNodes

vector describing the number of the successive elements connecting the network

nbCovariates

integer, the number of covariates

blockProp

block proportions (aka prior probabilities of each block)

connectParam

parameters associated to the connectivity of the SBM, e.g. matrix of inter/inter block probabilities when model is Bernoulli

covarParam

vector of regression parameters associated with the covariates.

covarList

list of matrices of covariates

covarArray

the array of covariates

covarEffect

effect of covariates

networkData

the network data (adjacency or incidence matrix or list of such object)

expectation

expected values of connection under the current model

Methods

Public methods

Method new()

constructor for SBM

Usage
SBM$new(
  model = vector("character", 0),
  directed = vector("logical", 0),
  dimension = vector("numeric", 0),
  dimLabels = vector("character", 0),
  blockProp = vector("numeric", 0),
  connectParam = vector("list", 0),
  covarParam = numeric(length(covarList)),
  covarList = list()
)
Arguments
model

character describing the type of model

directed

logical describing if the network data is directed or not

dimension

dimension of the network data

dimLabels

labels of each dimension

blockProp

parameters for block proportions (vector or list of vectors)

connectParam

list of parameters for connectivity

covarParam

optional vector of covariates effect

covarList

optional list of covariates data

Method rNetwork()

a method to sample a network data for the current SBM (blocks and edges)

Usage
SBM$rNetwork(store = FALSE)
Arguments
store

should the sampled network be stored (and overwrite the existing data)? Default to FALSE

Returns

a list with the sampled block and network

Method show()

print method

Usage
SBM$show(type = "Stochastic Block Model")
Arguments
type

character to tune the displayed name

Method print()

print method

Usage
SBM$print()

Method clone()

The objects of this class are cloneable with this method.

Usage
SBM$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

R6 class for Simple SBM

Description

R6 class for Simple SBM

R6 class for Simple SBM

Super class

sbm::SBM -> SimpleSBM

Active bindings

dimLabels

a single character giving the label of the nodes

blockProp

vector of block proportions (aka prior probabilities of each block)

connectParam

parameters associated to the connectivity of the SBM, e.g. matrix of inter/inter block probabilities when model is Bernoulli

probMemberships

matrix of estimated probabilities for block memberships for all nodes

nbBlocks

number of blocks

nbDyads

number of dyads (potential edges in the network)

nbConnectParam

number of parameter used for the connectivity

memberships

vector of clustering

indMemberships

matrix for clustering memberships

Methods

Public methods

Inherited methods

Method new()

constructor for SBM

Usage
SimpleSBM$new(
  model,
  nbNodes,
  directed,
  blockProp,
  connectParam,
  dimLabels = c("node"),
  covarParam = numeric(length(covarList)),
  covarList = list()
)
Arguments
model

character describing the type of model

nbNodes

number of nodes in the network

directed

logical, directed network or not.

blockProp

parameters for block proportions (vector of list of vectors)

connectParam

list of parameters for connectivity with a matrix of means 'mean' and an optional scalar for the variance 'var'. The size of mu must match blockProp length

dimLabels

optional label for the node (default is "nodeName")

covarParam

optional vector of covariates effect

covarList

optional list of covariates data

Method rMemberships()

a method to sample new block memberships for the current SBM

Usage
SimpleSBM$rMemberships(store = FALSE)
Arguments
store

should the sampled blocks be stored (and overwrite the existing data)? Default to FALSE

Returns

the sampled blocks

Method rEdges()

a method to sample a network data (edges) for the current SBM

Usage
SimpleSBM$rEdges(store = FALSE)
Arguments
store

should the sampled edges be stored (and overwrite the existing data)? Default to FALSE

Returns

the sampled network

Method predict()

prediction under the currently parameters

Usage
SimpleSBM$predict(covarList = self$covarList, theta_p0 = 0)
Arguments
covarList

a list of covariates. By default, we use the covariates with which the model was estimated

theta_p0

a threshold...

Returns

a matrix of expected values for each dyad

Method show()

show method

Usage
SimpleSBM$show(type = "Simple Stochastic Block Model")
Arguments
type

character used to specify the type of SBM

Method plot()

basic matrix plot method for SimpleSBM object or mesoscopic plot

Usage
SimpleSBM$plot(
  type = c("data", "expected", "meso"),
  ordered = TRUE,
  plotOptions = list()
)
Arguments
type

character for the type of plot: either 'data' (true connection), 'expected' (fitted connection) or 'meso' (mesoscopic view). Default to 'data'.

ordered

logical: should the rows and columns be reordered according to the clustering? Default to TRUE.

plotOptions

list with the parameters for the plot. See help of the corresponding S3 method for details.

Returns

a ggplot2 object for the 'data' and 'expected', a list with the igraph object g, the layout and the plotOptions for the 'meso'

Method clone()

The objects of this class are cloneable with this method.

Usage
SimpleSBM$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

R6 Class definition of a Simple SBM fit

Description

R6 Class definition of a Simple SBM fit

R6 Class definition of a Simple SBM fit

Details

This class is designed to give a representation and adjust an SBM fitted with blockmodels.

Super classes

sbm::SBM -> sbm::SimpleSBM -> SimpleSBM_fit

Active bindings

loglik

double: approximation of the log-likelihood (variational lower bound) reached

ICL

double: value of the integrated classification log-likelihood

penalty

double, value of the penalty term in ICL

entropy

double, value of the entropy due to the clustering distribution

storedModels

data.frame of all models fitted (and stored) during the optimization

Methods

Public methods

Inherited methods

Method new()

constructor for a Simple SBM fit

Usage
SimpleSBM_fit$new(
  adjacencyMatrix,
  model,
  directed,
  dimLabels = c(node = "nodeName"),
  covarList = list()
)
Arguments
adjacencyMatrix

square (weighted) matrix

model

character ('bernoulli', 'poisson', 'gaussian')

directed

logical, directed network or not. In not, adjacencyMatrix must be symmetric.

dimLabels

list of labels of each dimension (in row, in columns)

covarList

and optional list of covariates, each of whom must have the same dimension as adjacencyMatrix

Method optimize()

function to perform optimization

Usage
SimpleSBM_fit$optimize(estimOptions = list())
Arguments
estimOptions

a list of parameters controlling the inference algorithm and model selection. See details.

Method setModel()

method to select a specific model among the ones fitted during the optimization. Fields of the current SBM_fit will be updated accordingly.

Usage
SimpleSBM_fit$setModel(index)
Arguments
index

integer, the index of the model to be selected (row number in storedModels)

Method reorder()

permute group labels by order of decreasing probability

Usage
SimpleSBM_fit$reorder()

Method show()

show method

Usage
SimpleSBM_fit$show(type = "Fit of a Simple Stochastic Block Model")
Arguments
type

character used to specify the type of SBM

Method clone()

The objects of this class are cloneable with this method.

Usage
SimpleSBM_fit$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Extract model coefficients

Description

Extracts model coefficients from objects with class SBM and children (SimpleSBM_fit, BipartiteSBM_fit)

Usage

## S3 method for class 'SBM'
coef(object, type = c("connectivity", "block", "covariates"), ...)

Arguments

object

an R6 object inheriting from class SBM_fit (like SimpleSBM_fit or BipartiteSBM_fit)

type

type of parameter that should be extracted. Either 'block' for

\pi

, 'connectivity' for

\theta

, or "covariates" for

\beta

. Default is 'connectivity'.

...

additional parameters for S3 compatibility. Not used

Value

vector or list of parameters.

Define a network

Description

Define a network

Usage

defineSBM(
  netMat,
  model = "bernoulli",
  type = ifelse(ncol(netMat) == nrow(netMat), "simple", "bipartite"),
  directed = !isSymmetric(netMat),
  dimLabels = c(row = "row", col = "col"),
  covariates = list()
)

Arguments

netMat

a matrix describing the network: either an adjacency (square) or incidence matrix with possibly weighted entries.

model

character describing the model for the relation between nodes ('bernoulli', 'poisson', 'gaussian', ...). Default is 'bernoulli'.

type

Type of the matrix, choice between 'simple' and 'bipartite'

directed

logical: is the network directed or not? Only relevant when type is 'Simple'. Default is TRUE if netMat is symmetric, FALSE otherwise

dimLabels

an optional vector of labels for each dimension (in row, in column). Default value = c('row' = row,'col'= col)

covariates

a list of matrices with same dimension as mat describing covariates at the edge level. No covariate per Default.

Value

an object SimpleSBM or BipartiteSBM with the informations required to define a future multipartite network

Examples

A <- matrix(rbinom(100,1,.2), 10, 10)
myNet <- defineSBM(A, "poisson", "simple", TRUE, "Actor")

Estimation of Bipartite SBMs

Description

This function performs variational inference of bipartite Stochastic Block Models, with various model for the distribution of the edges: Bernoulli, Poisson, or Gaussian models.

Usage

estimateBipartiteSBM(
  netMat,
  model = "bernoulli",
  dimLabels = c(row = "row", col = "col"),
  covariates = list(),
  estimOptions = list()
)

Arguments

netMat

a matrix describing the network: either an adjacency (square) or incidence matrix with possibly weighted entries.

model

character describing the model for the relation between nodes ('bernoulli', 'poisson', 'gaussian', ...). Default is 'bernoulli'.

dimLabels

an optional vector of labels for each dimension (in row, in column)

covariates

a list of matrices with same dimension as mat describing covariates at the edge level. No covariate per Default.

estimOptions

a list of parameters controlling the inference algorithm and model selection. See details.

Details

The list of parameters estimOptions essentially tunes the optimization process and the variational EM algorithm, with the following parameters

Value

a list with the estimated parameters. See details...

Examples

### =======================================
### BIPARTITE BINARY SBM (Bernoulli model)

## Graph parameters and Sampling
nbNodes <- c(60, 80)
blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions
means <- matrix(runif(6), 2, 3)  # connectivity matrix
# In Bernoulli SBM, parameters is a list with a
# matrix of means 'mean' which are probabilities of connection
connectParam <- list(mean = means)
mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'bernoulli')

## Estimation
myBipartiteSBM <- estimateBipartiteSBM(mySampler$networkData, estimOptions = list(plot = FALSE))
plot(myBipartiteSBM, 'expected')

### =======================================
### BIPARTITE POISSON SBM

## Graph parameters & Sampling
nbNodes <- c(60, 80)
blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions
means <- matrix(rbinom(6, 30, 0.25), 2, 3)  # connectivity matrix
connectParam <- list(mean = means)
mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'poisson')

## Estimation
myBipartiteSBM <-
  estimateBipartiteSBM(mySampler$networkData, 'poisson', estimOptions = list(plot = FALSE))
plot(myBipartiteSBM, 'expected')

### =======================================
### BIPARTITE GAUSSIAN SBM
## Graph parameters & sampling
nbNodes <- c(60, 80)
blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions
means <- 20 * matrix(runif(6), 2, 3)  # connectivity matrix
connectParam <- list(mean = means, var = 1)
mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'gaussian')

## Estimation
myBipartiteSBM <-
  estimateBipartiteSBM(mySampler$networkData, 'gaussian', estimOptions = list(plot = FALSE))
plot(myBipartiteSBM, 'expected')

Estimation for multipartite SBM

Description

Estimation for multipartite SBM

Usage

estimateMultipartiteSBM(listSBM, estimOptions = list())

Arguments

listSBM

list of networks that were defined by the defineSBM function

estimOptions

options for the inference procedure

Details

The list of parameters estimOptions essentially tunes the optimization process and the variational EM algorithm, with the following parameters

Value

a MultipartiteSBM_fit object with the estimated parameters and the blocks in each Functional Group

Examples

## Not run: 
## About the Parts/Functional Groups (FG)
blockProp <- list(c(0.16 ,0.40 ,0.44),c(0.3,0.7)) # prop of blocks in each FG
archiMultipartite <-  rbind(c(1,2),c(2,2),c(1,1)) # architecture of the multipartite net.
nbNodes <- c(60,50)
## About the connection matrices
directed <- c(NA, TRUE, FALSE) # type of each network
model <- c('gaussian','bernoulli','poisson')
C1 <-
 list(mean = matrix(c(6.1, 8.9, 6.6, 9.8, 2.6, 1.0), 3, 2),
      var  = matrix(c(1.6, 1.6, 1.8, 1.7 ,2.3, 1.5),3, 2))
C2 <- list(mean = matrix(c(0.7,1.0, 0.4, 0.6),2, 2))
m3 <- matrix(c(2.5, 2.6 ,2.2 ,2.2, 2.7 ,3.0 ,3.6, 3.5, 3.3),3,3 )
C3 <- list(mean = .5 * (m3 + t(m3)))
connectParam <- list(C1, C2, C3)
## Graph Sampling
mySampleMSBM <- sampleMultipartiteSBM(nbNodes, blockProp,
                                      archiMultipartite, connectParam, model,
                                      directed, dimLabels = c('A','B'), seed = 2)
listSBM <- mySampleMSBM$listSBM
estimOptions <- list(initBM = FALSE, nbCores  = 2)
myMSBM <- estimateMultipartiteSBM(listSBM, estimOptions)
plot(myMSBM, type = "data")
plot(myMSBM, type = "expected")
plot(myMSBM, type = "meso")

## End(Not run)

Estimation for Multiplex SBM

Description

Estimation for Multiplex SBM

Usage

estimateMultiplexSBM(listSBM, dependent = FALSE, estimOptions = list())

Arguments

listSBM

list of networks that were defined by the defineSBM function

dependent

logical parameter indicating whether the networks in the multiplex structure are dependent beyond the latent variables,

estimOptions

options for the inference procedure

Details

The list of parameters estimOptions essentially tunes the optimization process and the variational EM algorithm, with the following parameters

Value

a MultiplexSBM_fit object with the estimated parameters and the blocks

Examples

## Not run: 
### =======================================
### MULTIPLEX SBM without dependence between layers
##
Nnodes <- 40
blockProp <- c(.4,.6)
nbLayers <- 2
connectParam <- list(list(mean=matrix(rbeta(4,.5,.5),2,2)),list(mean=matrix(rexp(4,.5),2,2)))
model <- c("bernoulli","poisson")
type <- "directed"
mySampleMultiplexSBM <-
   sampleMultiplexSBM(
   nbNodes = Nnodes,
    blockProp = blockProp,
   nbLayers = nbLayers,
   connectParam = connectParam,
   model=model,
   type=type)
listSBM <- mySampleMultiplexSBM$listSBM
estimOptions <- list(initBM = FALSE, nbCores  = 2)
myMultiplexSBM <- estimateMultiplexSBM(listSBM,estimOptions,dependent=FALSE)
### =======================================
### MULTIPLEX SBM Gaussian with dependence
##
Q <- 3
nbLayers <- 2
connectParam <- list()
connectParam$mu <- vector("list",nbLayers)
connectParam$mu[[1]] <-  matrix(.1,Q,Q) + diag(1:Q)
connectParam$mu[[2]] <- matrix(-2,Q,Q) + diag(rev(Q:1))
connectParam$Sigma <- matrix(c(2,1,1,4),nbLayers,nbLayers)
model <- rep("gaussian",2)
type <- "directed"
Nnodes <- 80
blockProp <- c(.3,.3,.4)
mySampleMultiplexSBM <-
  sampleMultiplexSBM(
     nbNodes = Nnodes,
     blockProp = blockProp,
     nbLayers = nbLayers,
     connectParam = connectParam,
     model=model,
     type="undirected",
     dependent=TRUE)
listSBM <- mySampleMultiplexSBM$listSBM
myMultiplexSBM <- estimateMultiplexSBM(listSBM,estimOptions,dependent=TRUE)
## MultiplexSBM Bernoulli with dependence
Q <- 2
P00<-matrix(runif(Q*Q),Q,Q)
P10<-matrix(runif(Q*Q),Q,Q)
P01<-matrix(runif(Q*Q),Q,Q)
P11<-matrix(runif(Q*Q),Q,Q)
SumP<-P00+P10+P01+P11
P00<-P00/SumP
P01<-P01/SumP
P10<-P10/SumP
P11<-P11/SumP
connectParam <- list()
connectParam$prob00 <- P00
connectParam$prob01 <- P01
connectParam$prob10 <- P10
connectParam$prob11 <- P11
model <- rep("bernoulli",2)
type <- "directed"
nbLayers <- 2
Nnodes <- 40
blockProp <- c(.6,.4)
mySampleMultiplexSBM <-
   sampleMultiplexSBM(
     nbNodes = Nnodes,
     blockProp = blockProp,
     nbLayers = nbLayers,
     connectParam = connectParam,
     model=model,
     type=type,
     dependent=TRUE)
listSBM <- mySampleMultiplexSBM$listSBM
myMultiplexSBM <- estimateMultiplexSBM(listSBM,estimOptions,dependent=TRUE)

## End(Not run)

Estimation of Simple SBMs

Description

This function performs variational inference of simple Stochastic Block Models, with various model for the distribution of the edges: Bernoulli, Poisson, or Gaussian models.

Usage

estimateSimpleSBM(
  netMat,
  model = "bernoulli",
  directed = !isSymmetric(netMat),
  dimLabels = c("node"),
  covariates = list(),
  estimOptions = list()
)

Arguments

netMat

a matrix describing the network: either an adjacency (square) or incidence matrix with possibly weighted entries.

model

character describing the model for the relation between nodes ('bernoulli', 'poisson', 'gaussian', ...). Default is 'bernoulli'.

directed

logical: is the network directed or not? Only relevant when type is 'Simple'. Default is TRUE if netMat is symmetric, FALSE otherwise

dimLabels

an optional label for referring to the nodes

covariates

a list of matrices with same dimension as mat describing covariates at the edge level. No covariate per Default.

estimOptions

a list of parameters controlling the inference algorithm and model selection. See details.

Details

The list of parameters estimOptions essentially tunes the optimization process and the variational EM algorithm, with the following parameters

Value

a list with the estimated parameters. See details...

Examples

### =======================================
### SIMPLE BINARY SBM (Bernoulli model)

## Graph parameters & Sampling
nbNodes  <- 60
blockProp <- c(.5, .25, .25) # group proportions
means <- diag(.4, 3) + 0.05  # connectivity matrix: affiliation network
connectParam <- list(mean = means)
mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam)
adjacencyMatrix <- mySampler$networkData

## Estimation
mySimpleSBM <-
  estimateSimpleSBM(adjacencyMatrix, 'bernoulli', estimOptions = list(plot = FALSE))
plot(mySimpleSBM, 'data', ordered = FALSE)
plot(mySimpleSBM, 'data')
plot(mySimpleSBM, 'expected', ordered = FALSE)
plot(mySimpleSBM, 'expected')
plot(mySimpleSBM, 'meso')

### =======================================
### SIMPLE POISSON SBM

## Graph parameters & Sampling
nbNodes  <- 60
blockProp <- c(.5, .25, .25) # group proportions
means <- diag(15., 3) + 5    # connectivity matrix: affiliation network
connectParam <- list(mean = means)
mySampler <- sampleSimpleSBM(nbNodes, blockProp, list(mean = means), model = "poisson")
adjacencyMatrix <- mySampler$networkData

## Estimation
mySimpleSBM <- estimateSimpleSBM(adjacencyMatrix, 'poisson',
   estimOptions = list(plot = FALSE))
plot(mySimpleSBM, 'data', ordered = FALSE)
plot(mySimpleSBM, 'data')
plot(mySimpleSBM, 'expected', ordered = FALSE)
plot(mySimpleSBM, 'expected')

### =======================================
### SIMPLE GAUSSIAN SBM

## Graph parameters & Sampling
nbNodes  <- 60
blockProp <- c(.5, .25, .25)      # group proportions
means <- diag(15., 3) + 5 # connectivity matrix: affiliation network
connectParam <- list(mean = means, var = 2)
mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam, model = "gaussian")

## Estimation
mySimpleSBM <-
   estimateSimpleSBM(mySampler$networkData, 'gaussian', estimOptions = list(plot = FALSE))
plot(mySimpleSBM, 'data', ordered = FALSE)
plot(mySimpleSBM, 'data')
plot(mySimpleSBM, 'expected', ordered = FALSE)
plot(mySimpleSBM, 'expected')

Extract model fitted values

Description

Extracts fitted values for object with class (SimpleSBM_fit, BipartiteSBM_fit) or multipartitepartiteSBM_fit)

Usage

## S3 method for class 'SBM'
fitted(object, ...)

Arguments

object

an R6 object inheriting from SimpleSBM_fit, BipartiteSBM_fit or MultipartiteSBM_fit

...

additional parameters for S3 compatibility. Not used

Value

a matrix of expected fitted values for each dyad

fungus-tree interaction network

Description

This data set provides information about $154$ fungi sampled on $51$ tree species.

Usage

fungusTreeNetwork

Format

A list with the following entries:

Source

Vacher, Corinne, Dominique Piou, and Marie-Laure Desprez-Loustau. "Architecture of an antagonistic tree/fungus network: the asymmetric influence of past evolutionary history." PloS one 3.3 (2008): e1740.

Auxiliary function to check the given class of an object

Description

Auxiliary function to check the given class of an object

Usage

is_SBM(Robject)

Arguments

Robject

an R6 object inheriting from class SBM

Value

TRUE or FALSE

Ecological multipartite interaction network

Description

Multipartite network of mutualistic interactions between plants and pollinators, plants and birds and plants and ants.

Usage

multipartiteEcologicalNetwork

Format

A list a 3 binary incidence matrices

Source

Dataset compiled and conducted at Centro de Investigaciones Costeras La Mancha (CICOLMA), located on the central coast of the Gulf of Mexico, Veracruz, Mexico. see doi:10.1098/rspb.2016.1564 and https://github.com/lucaspdmedeiros/multi-network_core_removal/tree/master/data

SBM Plot

Description

Basic matrix plot method for SBM object or mesoscopic view

Usage

## S3 method for class 'SBM'
plot(
  x,
  type = c("data", "expected", "meso"),
  ordered = TRUE,
  plotOptions = list(),
  ...
)

Arguments

x

an object inheriting from class SBM

type

character for the type of plot: either 'data' (true connection), 'expected' (fitted connection) or 'meso' (mesoscopic). Default to 'data'.

ordered

logical: should the rows and columns be ordered according to the clustering? Default to TRUE (not taken into account for 'meso').

plotOptions

list with parameters for 'meso' type plot and data type plot. Details are given below

...

additional parameters for S3 compatibility. Not used

Details

The list of parameters plotOptions for the mesoscopic plot is:

"seed":

seed to control the layout

"title":

character string for the title. Default value is NULL

"layout":

Default value = NULL

"vertex.color":

Default value is "salmon2"

"vertex.frame.color":

Node border color.Default value is "black"

"vertex.shape":

One of "none", "circle", "square", "csquare", "rectangle" "crectangle", "vrectangle", "pie", "raster", or "sphere". Default value = "circle"

"vertex.size":

Size of the node (default is 2)

"vertex.size2":

The second size of the node (e.g. for a rectangle)

"vertex.label.name":

Names of the vertices. Default value is the label of the nodes

"vertex.label.color":

Default value is "black"

"vertex.label.font":

Default value is 2. Font: 1 plain, 2 bold, 3, italic, 4 bold italic, 5 symbol

"vertex.label.cex":

Font size (multiplication factor, device-dependent).Default value is 0.9.

"vertex.label.dist":

Distance between the label and the vertex. Default value is 0

"vertex.label.degree":

The position of the label in relation to the vertex. default value is 0

"edge.threshold":

Threshold under which the edge is not plotted. Default value is = -Inf

"edge.color":

Default value is "gray"

"edge.width":

Factor parameter. Default value is 10

"edge.arrow.size":

Default value is 1

"edge.arrow.width":

Default value is 2

"edge.lty":

Line type, could be 0 or "blank", 1 or "solid", 2 or "dashed", 3 or "dotted", 4 or "dotdash", 5 or "longdash", 6 or "twodash". Default value is "solid"

"edge.curved":

Default value is = 0.3.

For type = 'data' or 'expected plot', the list of parameters plotOptions is

"legend":

Boolean. Set TRUE if you want to see the legend. Default value is FALSE

"legend.title":

Boolean. Set TRUE if you want to print the title of the legend. Default value is FALSE

"legend.position":

Position of the legend. Possible values are 'bottom', 'top','left,'right'. Default value is 'bottom'

"rowNames":

Set true if the rownames must be plotted. Default value is FALSE

"colNames":

Set true if the colNames must be plotted. Default value is FALSE

"line.color":

Chain of character. The color of the lines to separate groups if a clustering is provided. Default value is red

"line.width":

Numeric. Width of the lines to separate groups. Default value is NULL, automatically chosen

"title":

Chain of character. Title of the plot. Default value is NULL

Value

a ggplot2 object for the 'data' and 'expected', a list with the igraph object g and the layout for the 'meso'

Plot an alluvial plot between clusterings

Description

Plot an alluvial plot between clusterings

Usage

plotAlluvial(listMemberships, plotOptions = list())

Arguments

listMemberships

: a list vectors containing the memberships

plotOptions

: a list containing the options for Alluvial plots

Details

The list of parameters plotOptions provides the following options

Value

display the alluvial plot, returns the plotOptions as a list

Examples

listMemberships <- list(C1 = rep(c('A','B','C'),each=10),C2 = rep(c(1,2,4),10))
plotAlluvial(listMemberships)

Plot an adjacency or incidence Matrix

Description

Plot an adjacency or incidence Matrix

Usage

plotMyMatrix(
  Mat,
  dimLabels = c(row = "row", col = "col"),
  clustering = NULL,
  plotOptions = NULL
)

Arguments

Mat

: a matrix representing the network

dimLabels

: a vector of length 1 or 2 specifying the types of nodes in row and col (functional group) (Default is NULL)

clustering

: a list of length 2 specifying a clustering on row and col

plotOptions

: a list providing options. See details below.

Details

The list of parameters plotOptions for the matrix plot is

Value

a ggplot object corresponding to the plot

Examples

M <- matrix(sample(c(0,1),900,replace=TRUE),30,30)
plotMyMatrix(M, dimLabels = c('individulals'), plotOptions= list(legend = FALSE))
M2 <- matrix( rpois(800,10),40,20)
plotMyMatrix(M2, dimLabels = c(row = 'reader',col = 'book'), plotOptions = list(legend = TRUE))

Plot the matrices corresponding to a Multipartite Network

Description

Plot the matrices corresponding to a Multipartite Network

Usage

plotMyMultipartiteMatrix(listSBM, memberships = NULL, plotOptions = list())

Arguments

listSBM

: a list of objects representing the multipartite network (see)

memberships

: a list of length equal to the number of Functional Groups providing the clusterings inside each group.

plotOptions

: a list containing the options. See details.

Details

plotOptions is a list containing the following items

Value

a ggplot object corresponding to the plot

Examples

data("multipartiteEcologicalNetwork")
Net <- multipartiteEcologicalNetwork
type='bipartite'
model = 'bernoulli'
directed = FALSE
listNet <- list()
listNet[[1]] = defineSBM(Net$Inc_plant_ant,
                         model,type,directed,
                         dimLabels = c(row = "Plants", col = "Ants"))
listNet[[2]] = defineSBM(Net$Inc_plant_bird,model,type,directed,
                      dimLabels =c(row = "Plants",col = "Birds"))
plotMyMultipartiteMatrix(listNet,plotOptions=list(legend = TRUE,title='Ecology'))

listNet <- list()
listNet[[1]] <- defineSBM(matrix(rbinom(1000,1,0.5),20,50),
                   model = 'bernoulli',
                   type  ='bipartite', directed = NA,
                   dimLabels = c(row="Questions",col="Students"))
listNet[[2]] <- defineSBM(matrix(rpois(20*30,8),30,20),
                   model = 'poisson',
                   type  ='bipartite',directed = NA,
                   dimLabels = c(row="Competences",col="Questions"))
plotMyMultipartiteMatrix(listNet,plotOptions=list(legend = TRUE,compact = FALSE))
plotMyMultipartiteMatrix(listNet,plotOptions=list(legend = TRUE,normalized =  TRUE))

Plot the matrices corresponding to a Multiplex Network

Description

Plot the matrices corresponding to a Multiplex Network

Usage

plotMyMultiplexMatrix(listSBM, memberships = NULL, plotOptions = list())

Arguments

listSBM

: a list of objects representing the multiplex network (see)

memberships

: a list of length equal to the number of Functional Groups providing the clusterings inside each group.

plotOptions

: a list containing the options. See details.

Details

plotOptions is a list containing the following items

Value

a ggplot object corresponding to the plot

Examples

Nnodes <- c(40,30)
blockProp <- list(c(.4,.6),c(0.5,0.5))
nbLayers <- 2
connectParam <- list(list(mean=matrix(rbeta(4,.5,.5),2,2)),list(mean=matrix(rexp(4,.5),2,2)))
names(connectParam) <- c('Read','Score')
model <- c("bernoulli","poisson")
type <- "bipartite"
mySampleMultiplexSBM <-
 sampleMultiplexSBM(
   nbNodes = Nnodes,
   blockProp = blockProp,
   nbLayers = nbLayers,
   connectParam = connectParam,
   model=model,
   dimLabels =  c('readers','books'),
   type=type)
listNet <- mySampleMultiplexSBM$listSBM
names(listNet) <- c("Read","Affinity")
plotMyMultiplexMatrix(listNet,plotOptions=list(legend = TRUE))

Model Predictions

Description

Make predictions from an SBM.

Usage

## S3 method for class 'SBM'
predict(object, covarList = object$covarList, theta_p0 = 0, ...)

Arguments

object

an R6 object inheriting from class SBM_fit (like SimpleSBM_fit or BipartiteSBM_fit)

covarList

a list of covariates. By default, we use the covariates associated with the model.

theta_p0

a threshold...

...

additional parameters for S3 compatibility. Not used

Value

a matrix of expected values for each dyad

Sampling of Bipartite SBMs

Description

This function samples a simple Stochastic Block Models, with various model for the distribution of the edges: Bernoulli, Poisson, or Gaussian models, and possibly with covariates

Usage

sampleBipartiteSBM(
  nbNodes,
  blockProp,
  connectParam,
  model = "bernoulli",
  dimLabels = c(row = "row", col = "col"),
  covariates = list(),
  covariatesParam = numeric(0)
)

Arguments

nbNodes

number of nodes in the network

blockProp

parameters for block proportions: list of size two with row and column block proportions

connectParam

list of parameters for connectivity with a matrix of means 'mean' and an optional matrix of variances 'var', the sizes of which must match blockProp length (in row, respectively in column)

model

character describing the model for the relation between nodes ('bernoulli', 'poisson', 'gaussian', 'ZIgaussian'). Default is 'bernoulli'.

dimLabels

an optional list of labels for each dimension (in row, in column)

covariates

a list of matrices with same dimension as mat describing covariates at the edge level. No covariate per Default.

covariatesParam

optional vector of covariates effect. A zero length numeric vector by default.

Value

an object with class BipartiteSBM

Examples

### =======================================
### BIPARTITE BERNOULLI SBM
## Graph parameters
nbNodes <- c(100, 120)
blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions
means <- matrix(runif(6), 2, 3)  # connectivity matrix
# In Bernoulli SBM, parameters is a list with
# a matrix of means 'mean' which are probabilities of connection
connectParam <- list(mean = means)

## Graph Sampling
dimLabels = c(row='Reader',col='Book')
mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'bernoulli',dimLabels)
plot(mySampler)
plot(mySampler,type='meso',plotOptions = list(vertex.label.name=list(row='Reader',col='Book')))
plot(mySampler,type='meso',plotOptions = list(vertex.label.name=c('A','B'),vertex.size = 1.4))
mySampler$rMemberships() # sample new memberships
mySampler$rEdges()   # sample new edges
mySampler$rNetwork()   # sample a new networrk (blocks and edges)
### =======================================
### BIPARTITE POISSON SBM
## Graph parameters
nbNodes <- c(100, 120)
blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions
means <- matrix(rbinom(6, 30, 0.25), 2, 3)  # connectivity matrix
# In Poisson SBM, parameters is a list with a matrix of
# means 'mean' which are a mean integer value taken by edges
connectParam <- list(mean = means)

## Graph Sampling
dimLabels = c(row = 'Ind', col = 'Service')
mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'poisson', dimLabels)
plot(mySampler,type='expected')
plotOptions = list(vertex.label.name=c('U','V'),vertex.size = c(1.4,1.3))
plot(mySampler, type='meso', plotOptions = plotOptions)
hist(mySampler$networkData)

### =======================================
### BIPARTITE GAUSSIAN SBM
## Graph parameters
nbNodes <- c(100, 120)
blockProp <- list(c(.5, .5), c(1/3, 1/3, 1/3)) # group proportions
means <- 20 * matrix(runif(6), 2, 3)  # connectivity matrix
# In Gaussian SBM, parameters is a list with a matrix
# of means 'mean' and a matrix of variances 'var'
connectParam <- list(mean = means, var = 1)

## Graph Sampling
mySampler <- sampleBipartiteSBM(nbNodes, blockProp, connectParam, model = 'gaussian')
plot(mySampler)
hist(mySampler$networkData)

Sampling of Multipartite SBMs

Description

This function samples a Multipartite Stochastic Block Models, with various model for the distribution of the edges: Bernoulli, Poisson, or Gaussian models

Usage

sampleMultipartiteSBM(
  nbNodes,
  blockProp,
  archiMultipartite,
  connectParam,
  model,
  directed,
  dimLabels = NULL,
  seed = NULL
)

Arguments

nbNodes

number of nodes in each functional group involved in the multipartite network

blockProp

a list of parameters for block proportions in each functional group

archiMultipartite

a matrix with two columns and nbNetworks lines, each line specifying the index of the functional groups in interaction.

connectParam

list of parameters for connectivity (of length nbNetworks). Each element is a list of one or two elements: a matrix of means 'mean' and an optional matrix of variances 'var', the sizes of which must match blockProp length

model

a vector of characters describing the model for each network of the Multipartite relation between nodes ('bernoulli', 'poisson', 'gaussian', ...). Default is 'bernoulli'.

directed

a vector of logical, directed network or not for each network. Default is FALSE.

dimLabels

an optional list of labels for functional group involved in the network

seed

numeric to set the seed.

Value

a list of two elements : simulatedMemberships are the clustering of each node in each Functional Group, multipartiteNetwork is the list of the simulated networks (each one being a simple or bipartite network)

Examples

### =======================================
### MULTIPARTITE SBM  : 4 networks between 3 Functional Groups
## Graph parameters
# About the Functional Groups (FG)
nbNodes <-  c(100,50,40)
blockProp <- vector("list", 3)  # parameters of clustering in each functional group
blockProp[[1]] <- c(0.4,0.3,0.3) # in Functional Group 1
blockProp[[2]] <- c(0.6,0.4) # in Functional Group 2
blockProp[[3]]  <- c(0.6,0.4) # in Functional Group 3
# About the interactions between the FG
archiMultipartite  <-  rbind(c(1,2),c(2,3),c(2,2),c(1,3)) #
model <- c('bernoulli','poisson','gaussian','gaussian') # type of distribution in each network
# for each network : directed or not (not required for an interaction between two different FG)
directed <- c( NA, NA  ,  FALSE , NA)
connectParam <- list()
connectParam[[1]] <- list(mean = matrix(c(0.3, 0.3, 0.5, 0.2, 0.6, 0.6),3,2))
connectParam[[2]] <- list(mean = matrix(c(1000 , 500,  400 , 950),2,2))
connectParam[[3]] <- list(mean = matrix(c(10, 0, -10, 20), 2,2), var = matrix(1,2,2))
connectParam[[4]] <- list(mean = matrix(c(3, 23 ,11 ,16 , 2 ,25), 3,2))
connectParam[[4]]$var <- matrix(c(10,20,1,5,0.1,10), 3,2)
dimLabels <- c('A','B','C')
## Graph Sampling
mySampleMBM <- sampleMultipartiteSBM(nbNodes, blockProp,
                                     archiMultipartite,
                                     connectParam, model, directed,
                                     dimLabels,seed = 3)
listSBM <- mySampleMBM$listSBM
memberships <- mySampleMBM$memberships
plotMyMultipartiteMatrix(listSBM)
plotMyMultipartiteMatrix(listSBM,plotOptions = list(normalized = TRUE))
plotMyMultipartiteMatrix(listSBM,memberships = memberships,plotOptions = list(normalized = TRUE))

Sampling of Multiplex SBMs

Description

This function samples a Multiplex Stochastic Block Models, with various model for the distribution of the edges: Bernoulli, Poisson, or Gaussian models

Usage

sampleMultiplexSBM(
  nbNodes,
  blockProp,
  nbLayers,
  connectParam,
  model,
  type = c("directed", "undirected", "bipartite"),
  dependent = FALSE,
  dimLabels = NULL,
  seed = NULL
)

Arguments

nbNodes

number of nodes in each functional group involved in the Multiplex network

blockProp

a vector for block proportion if the networks are simple, a list of parameters for block proportions for both functional groups if the networks are bipartite

nbLayers

a matrix with two columns and nbNetworks lines, each line specifying the index of the functional groups in interaction.

connectParam

list of parameters for connectivity (of length nbNetworks). Each element is a list of one or two elements: a matrix of means 'mean' and an optional matrix of variances 'var', the sizes of which must match blockProp length

model

a vector of characters describing the model for each network of the Multiplex relation between nodes ('bernoulli', 'poisson', 'gaussian', ...). Default is 'bernoulli'.

type

a string of character indicating whether the networks are directed, undirected or bipartite

dependent

connection parameters in each network

dimLabels

an optional list of labels for functional group involved in the network

seed

numeric to set the seed.

Value

a list of two elements : simulatedMemberships are the clustering of each node in each Functional Group, MultiplexNetwork is the list of the simulated networks (each one being a simple or bipartite network)

Examples

nbLayers <- 2

## MultiplexSBM without dependence between layers
Nnodes <- 40
blockProp <- c(.4,.6)
connectParam <- list(list(mean=matrix(rbeta(4,.5,.5),2,2)),list(mean=matrix(rexp(4,.5),2,2)))
model <- c("bernoulli","poisson")
type <- "directed"
mySampleMultiplexSBM <-
   sampleMultiplexSBM(
   nbNodes = Nnodes,
    blockProp = blockProp,
   nbLayers = nbLayers,
   connectParam = connectParam,
   model=model,
   type=type)
listSBM <- mySampleMultiplexSBM$listSBM

## MultiplexSBM Gaussian with dependence
Q <- 3
nbLayers <- 2
connectParam <- list()
connectParam$mu <- vector("list",nbLayers)
connectParam$mu[[1]] <-  matrix(.1,Q,Q) + diag(1:Q)
connectParam$mu[[2]] <- matrix(-2,Q,Q) + diag(rev(Q:1))
connectParam$Sigma <- matrix(c(2,1,1,4),nbLayers,nbLayers)
model <- rep("gaussian",2)
type <- "directed"
Nnodes <- 80
blockProp <- c(.3,.3,.4)
mySampleMultiplexSBM <-
  sampleMultiplexSBM(
     nbNodes = Nnodes,
     blockProp = blockProp,
     nbLayers = nbLayers,
     connectParam = connectParam,
     model=model,
     type="undirected",
     dependent=TRUE)
listSBM <- mySampleMultiplexSBM$listSBM
## MultiplexSBM Bernoulli with dependence
Q <- 2
P00<-matrix(runif(Q*Q),Q,Q)
P10<-matrix(runif(Q*Q),Q,Q)
P01<-matrix(runif(Q*Q),Q,Q)
P11<-matrix(runif(Q*Q),Q,Q)
SumP<-P00+P10+P01+P11
P00<-P00/SumP
P01<-P01/SumP
P10<-P10/SumP
P11<-P11/SumP
connectParam <- list()
connectParam$prob00 <- P00
connectParam$prob01 <- P01
connectParam$prob10 <- P10
connectParam$prob11 <- P11
model <- rep("bernoulli",2)
type <- "directed"
nbLayers <- 2
Nnodes <- 40
blockProp <- c(.6,.4)
mySampleMultiplexSBM <-
   sampleMultiplexSBM(
     nbNodes = Nnodes,
     blockProp = blockProp,
     nbLayers = nbLayers,
     connectParam = connectParam,
     model=model,
     type=type,
     dependent=TRUE)
listSBM_BB <- mySampleMultiplexSBM$listSBM

Sampling of Simple SBMs

Description

This function samples a simple Stochastic Block Models, with various model for the distribution of the edges: Bernoulli, Poisson, or Gaussian models, and possibly with covariates

Usage

sampleSimpleSBM(
  nbNodes,
  blockProp,
  connectParam,
  model = "bernoulli",
  directed = FALSE,
  dimLabels = c("node"),
  covariates = list(),
  covariatesParam = numeric(0)
)

Arguments

nbNodes

number of nodes in the network

blockProp

parameters for block proportions

connectParam

list of parameters for connectivity with a matrix of means 'mean' and an optional matrix of variances 'var', the sizes of which must match blockProp length

model

character describing the model for the relation between nodes ('bernoulli', 'poisson', 'gaussian', ...). Default is 'bernoulli'.

directed

logical, directed network or not. Default is FALSE.

dimLabels

an optional list of labels for each dimension (in row, in column)

covariates

a list of matrices with same dimension as mat describing covariates at the edge level. No covariate per Default.

covariatesParam

optional vector of covariates effect. A zero length numeric vector by default.

Value

an object with class SimpleSBM

Examples

### =======================================
### SIMPLE BINARY SBM (Bernoulli model)
## Graph parameters
nbNodes  <- 90
blockProp <- c(.5, .25, .25) # group proportions
means <- diag(.4, 3) + 0.05  # connectivity matrix: affiliation network
# In Bernoulli SBM, parameters is a list with a
# matrix of means 'mean' which are probabilities of connection
connectParam <- list(mean = means)

## Graph Sampling
mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam, model = 'bernoulli')
plot(mySampler)
plot(mySampler)
plot(mySampler,type='meso')
hist(mySampler$networkData)

### =======================================
### SIMPLE POISSON SBM
## Graph parameters
nbNodes  <- 90
blockProp <- c(.5, .25, .25) # group proportions
means <- diag(15., 3) + 5    # connectivity matrix: affiliation network
# In Poisson SBM, parameters is a list with
# a matrix of means 'mean' which are a mean integer value taken by edges
connectParam <- list(mean = means)

## Graph Sampling
mySampler <- sampleSimpleSBM(nbNodes, blockProp, list(mean = means), model = "poisson")
plot(mySampler)
plot(mySampler,type='meso')
hist(mySampler$networkData)

### =======================================
### SIMPLE GAUSSIAN SBM
## Graph parameters
nbNodes  <- 90
blockProp <- c(.5, .25, .25)      # group proportions
means <- diag(15., 3) + 5 # connectivity matrix: affiliation network
# In Gaussian SBM, parameters is a list with
# a matrix of means 'mean' and a matrix of variances 'var'
connectParam <- list(mean = means, var = 2)

## Graph Sampling
mySampler <- sampleSimpleSBM(nbNodes, blockProp, connectParam, model = "gaussian",dimLabels='Tree')
plot(mySampler)
plot(mySampler,type='meso')
hist(mySampler$networkData)

War data set

Description

This dataset contains two networks where the nodes are countries and an edge in network "belligerent" means that the two countries have been at least once at war between years 1816 to 2007 while an edge in network "alliance" means that the two countries have had a formal alliance between years 1816 to 2012. The network belligerent have less nodes since countries which have not been at war are not considered.

Usage

war

Format

A list with 2 two igraph objects, alliance and belligerent. Each graph have three attributes: 'name' (the country name), 'power' (a score related to military power: the higher, the better) and 'trade' (a score related to the trade effort between pairs of countries).

Source

networks were extracted from https://correlatesofwar.org/

References

Sarkees, Meredith Reid and Frank Wayman (2010). Resort to War: 1816 - 2007. Washington DC: CQ Press.

Gibler, Douglas M. 2009. International military alliances, 1648-2008. CQ Press

Examples

data(war)
class(war$belligerent)
igraph::gorder(war$alliance)
igraph::gorder(war$belligerent)
igraph::edges(war$alliance)
igraph::get.graph.attribute(war$alliance)