Package 'sbm'

Description

R6 class for Bipartite SBM

Super class

SBM -> BipartiteSBM

Active bindings

Methods

Public methods

• BipartiteSBM$new()

• BipartiteSBM$rMemberships()

• BipartiteSBM$rEdges()

• BipartiteSBM$predict()

• BipartiteSBM$show()

• BipartiteSBM$plot()

• BipartiteSBM$clone()

BipartiteSBM$new()

constructor for SBM

Usage

BipartiteSBM$new(
  model,
  nbNodes,
  blockProp = vector("list", 2),
  connectParam = list(mean = matrix(0, 0, 0)),
  dimLabels = c(row = "row", col = "col"),
  covarParam = numeric(length(covarList)),
  covarList = list(),
  nodesCovarList = vector("list", 2),
  nodesCovarParam = vector("list", 2)
)

Arguments

BipartiteSBM$rMemberships()

a method to sample new block memberships for the current SBM

Usage

BipartiteSBM$rMemberships(store = FALSE)

Arguments

Returns

the sampled blocks

BipartiteSBM$rEdges()

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

Usage

BipartiteSBM$rEdges(store = FALSE)

Arguments

Returns

the sampled network

BipartiteSBM$predict()

prediction under the current parameters

Usage

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

Arguments

BipartiteSBM$show()

show method

Usage

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

Arguments

BipartiteSBM$plot()

basic matrix plot method for BipartiteSBM object or mesoscopic plot

Usage

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

Arguments

Returns

a ggplot2 object

BipartiteSBM$clone()

The objects of this class are cloneable with this method.

Usage

BipartiteSBM$clone(deep = FALSE)

Arguments

Description

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

Details

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

• "nbCores integer for number of cores used. Default is 2 (1 under Positron, which does not allow forking)

• "verbosity" integer for verbosity (0, 1). Default is 1

• "plot" boolean, should the ICL be dynamically plotted or not. Default is TRUE, FALSE when "verbosity" is 0

• "exploreFactor" control the exploration of the number of groups

• "exploreMin" explore at least until exploreMin even if the exploration factor rule is achieved. Default 4. See the package blockmodels for details.

• "exploreMax" Stop exploration at exploreMax even if the exploration factor rule is not achieved. Default Inf. See the package blockmodels for details.

• "nbBlocksRange" minimal and maximal number or blocks explored

• "fast" logical: should approximation be used for Bernoulli model with covariates. Default to TRUE

Super classes

SBM -> BipartiteSBM -> BipartiteSBM_fit

Active bindings

Methods

Public methods

• BipartiteSBM_fit$new()

• BipartiteSBM_fit$optimize()

• BipartiteSBM_fit$setModel()

• BipartiteSBM_fit$reorder()

• BipartiteSBM_fit$show()

• BipartiteSBM_fit$clone()

BipartiteSBM_fit$new()

constructor for a Bipartite SBM fit

Usage

BipartiteSBM_fit$new(
  incidenceMatrix,
  model,
  dimLabels = c(row = "row", col = "col"),
  covarList = list(),
  nodesCovarList = vector("list", 2)
)

Arguments

BipartiteSBM_fit$optimize()

function to perform optimization

Usage

BipartiteSBM_fit$optimize(estimOptions = list())

Arguments

BipartiteSBM_fit$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

BipartiteSBM_fit$reorder()

permute group labels by order of decreasing probability

Usage

BipartiteSBM_fit$reorder()

BipartiteSBM_fit$show()

show method

Usage

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

Arguments

BipartiteSBM_fit$clone()

The objects of this class are cloneable with this method.

Usage

BipartiteSBM_fit$clone(deep = FALSE)

Arguments

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

Value

vector or list of parameters.

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

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, "bernoulli", "simple", TRUE, "Actor")

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(),
  nodesCovariates = vector("list", 2),
  estimOptions = list()
)

Arguments

Details

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

• "nbCores integer for number of cores used. Default is 2 (1 under Positron, which does not allow forking)

• "verbosity" integer for verbosity (0, 1). Default is 1

• "plot" boolean, should the ICL be dynamically plotted or not. Default is TRUE, FALSE when "verbosity" is 0

• "exploreFactor" control the exploration of the number of groups

• "exploreMin" explore at least until exploreMin even if the exploration factor rule is achieved. Default 4. See the package blockmodels for details.

• "exploreMax" Stop exploration at exploreMax even if the exploration factor rule is not achieved. Default Inf. See the package blockmodels for details.

• "nbBlocksRange" minimal and maximal number or blocks explored

• "fast" logical: should approximation be used for Bernoulli model with covariates. Default to TRUE

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')

Description

Estimation for multipartite SBM

Usage

estimateMultipartiteSBM(listSBM, estimOptions = list())

Arguments

Details

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

• "nbCores" integer for number of cores used. Default is 2 (1 under Positron, which does not allow forking)

• "verbosity" integer for verbosity (0, 1). Default is 1

• "nbBlocksRange" List of length the number of functional groups, each element supplying the minimal and maximal number of blocks to be explored. The names of the list must be the names of the functional groups. Default value is from 1 to 10)

• "initBM" Boolean. True if using simple and bipartite SBM as initialisations. Default value = TRUE

• "maxiterVEM" Number of max. number of iterations in the VEM. Default value = 100

• "maxiterVE" Number of max. number of iterations in the VE. Default value = 100

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)

Description

Estimation for Multiplex SBM

Usage

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

Arguments

Details

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

• "nbCores" integer for number of cores used. Default is 2 (1 under Positron, which does not allow forking)

• "verbosity" integer for verbosity (0, 1). Default is 1

• "nbBlocksRange" List of length the number of functional groups, each element supplying the minimal and maximal number of blocks to be explored. The names of the list must be the names of the functional groups. Default value is from 1 to 10)

• "initBM" Boolean. True if using simple and bipartite SBM as initialisations. Default value = TRUE

• "maxiterVEM" Number of max. number of iterations in the VEM. Default value = 100

• "maxiterVE" Number of max. number of iterations in the VE. Default value = 100

• "plot" boolean, should the ICL be dynamically plotted or not. Default is TRUE, FALSE when "verbosity" is 0. For dependent networks

• "exploreFactor" control the exploration of the number of groups. For dependent networks

• "exploreMin" explore at least until exploreMin even if the exploration factor rule is achieved. Default 4. See the package blockmodels for details. For dependent networks

• "exploreMax" Stop exploration at exploreMax even if the exploration factor rule is not achieved. Default Inf. See the package blockmodels for details. For dependent networks

• "nbBlocksRange" minimal and maximal number or blocks explored. For dependent networks

• "fast" logical: should approximation be used for Bernoulli model with covariates. Default to TRUE. For dependent networks

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)

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(),
  nodesCovariates = matrix(0, 0, 0),
  estimOptions = list()
)

Arguments

Details

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

• "nbCores integer for number of cores used. Default is 2 (1 under Positron, which does not allow forking)

• "verbosity" integer for verbosity (0, 1). Default is 1

• "plot" boolean, should the ICL be dynamically plotted or not. Default is TRUE, FALSE when "verbosity" is 0

• "exploreFactor" control the exploration of the number of groups

• "exploreMin" explore at least until exploreMin even if the exploration factor rule is achieved. Default 4. See the package blockmodels for details.

• "exploreMax" Stop exploration at exploreMax even if the exploration factor rule is not achieved. Default Inf. See the package blockmodels for details.

• "nbBlocksRange" minimal and maximal number or blocks explored

• "fast" logical: should approximation be used for Bernoulli model with covariates. Default to TRUE

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')

Description

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

Usage

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

Arguments

Value

a matrix of expected fitted values for each dyad

Description

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

Usage

fungusTreeNetwork

Format

A list with the following entries:

• fungi_list list of the fungus species names

• tree_list list of the tree species names

• fungus_tree binary fungus-tree interactions

• tree_tree weighted tree-tree interactions (number of common fungal species two tree species host)

• covar_tree covariates associated to pairs of trees (namely genetic, taxonomic and geographic distances)

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.

Description

Auxiliary function to check the given class of an object

Usage

is_SBM(Robject)

Arguments

Value

TRUE or FALSE

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

• Inc_plant_ant Interactions between plants (rows) and ants (cols). Matrix with 141 rows and 30 columns

• Inc_plant_bird Interactions between plants (rows) and birds (cols). Matrix with141 rows and 46 columns

• Inc_plant_flovis Interactions between plants (rows) and pollinators (cols). Matrix with 141 rows and 173 columns

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

Description

R6 Class definition of a Multipartite SBM

Super class

SBM -> MultipartiteSBM

Active bindings

Methods

Public methods

• MultipartiteSBM$new()

• MultipartiteSBM$show()

• MultipartiteSBM$print()

• MultipartiteSBM$plot()

• MultipartiteSBM$clone()

MultipartiteSBM$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

MultipartiteSBM$show()

print method

Usage

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

Arguments

MultipartiteSBM$print()

print method

Usage

MultipartiteSBM$print()

MultipartiteSBM$plot()

plot Multipartite Network

Usage

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

Arguments

MultipartiteSBM$clone()

The objects of this class are cloneable with this method.

Usage

MultipartiteSBM$clone(deep = FALSE)

Arguments

Description

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

Details

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

• "nbCores integer for number of cores used. Default is 2 (1 under Positron, which does not allow forking)

• "verbosity" integer for verbosity (0, 1). Default is 1

• "plot" boolean, should the ICL be dynamically plotted or not. Default is TRUE, FALSE when "verbosity" is 0

• "exploreFactor" control the exploration of the number of groups

• "exploreMin" explore at least until exploreMin even if the exploration factor rule is achieved. Default 4. See the package blockmodels for details.

• "exploreMax" Stop exploration at exploreMax even if the exploration factor rule is not achieved. Default Inf. See the package blockmodels for details.

• "nbBlocksRange" minimal and maximal number or blocks explored

• "fast" logical: should approximation be used for Bernoulli model with covariates. Default to TRUE

Super classes

SBM -> MultipartiteSBM -> MultipartiteSBM_fit

Active bindings

Methods

Public methods

• MultipartiteSBM_fit$new()

• MultipartiteSBM_fit$optimize()

• MultipartiteSBM_fit$predict()

• MultipartiteSBM_fit$setModel()

• MultipartiteSBM_fit$show()

• MultipartiteSBM_fit$clone()

MultipartiteSBM_fit$new()

constructor for Multipartite SBM

Usage

MultipartiteSBM_fit$new(netList)

Arguments

MultipartiteSBM_fit$optimize()

estimation of multipartiteSBM via GREMLINS

Usage

MultipartiteSBM_fit$optimize(estimOptions)

Arguments

MultipartiteSBM_fit$predict()

prediction under the currently estimated model

Usage

MultipartiteSBM_fit$predict()

Returns

a list of matrices matrix of expected values for each dyad

MultipartiteSBM_fit$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

MultipartiteSBM_fit$show()

show method

Usage

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

Arguments

MultipartiteSBM_fit$clone()

The objects of this class are cloneable with this method.

Usage

MultipartiteSBM_fit$clone(deep = FALSE)

Arguments

Description

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

• "nbCores" integer for number of cores used. Default is 2 (1 under Positron, which does not allow forking)

• "verbosity" integer for verbosity (0, 1). Default is 1

• "nbBlocksRange" List of length the number of functional groups, each element supplying the minimal and maximal number of blocks to be explored. The names of the list must be the names of the functional groups. Default value is from 1 to 10)

• "initBM" Boolean. True if using simple and bipartite SBM as initialisations. Default value = TRUE

• "maxiterVEM" Number of max. number of iterations in the VEM. Default value = 100

• "maxiterVE" Number of max. number of iterations in the VE. Default value = 100

Super classes

SBM -> MultipartiteSBM -> MultipartiteSBM_fit -> MultiplexSBM_fit

Active bindings

Methods

Public methods

• MultiplexSBM_fit$new()

• MultiplexSBM_fit$optimize()

• MultiplexSBM_fit$plot()

• MultiplexSBM_fit$show()

• MultiplexSBM_fit$predict()

• MultiplexSBM_fit$clone()

MultiplexSBM_fit$new()

constructor for Multiplex SBM

Usage

MultiplexSBM_fit$new(netList, dependentNet = FALSE)

Arguments

MultiplexSBM_fit$optimize()

estimation of multipartiteSBM via GREMLINS

Usage

MultiplexSBM_fit$optimize(estimOptions)

Arguments

MultiplexSBM_fit$plot()

plot Multiplex Network

Usage

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

Arguments

MultiplexSBM_fit$show()

show method

Usage

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

Arguments

MultiplexSBM_fit$predict()

prediction under the currently estimated model

Usage

MultiplexSBM_fit$predict()

Returns

a list of matrices matrix of expected values for each dyad

MultiplexSBM_fit$clone()

The objects of this class are cloneable with this method.

Usage

MultiplexSBM_fit$clone(deep = FALSE)

Arguments

Description

Basic matrix plot method for SBM object or mesoscopic view

Usage

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

Arguments

Details

For simple and bipartite SBM, the mesoscopic view draws the graphon as a network: each block is a node whose area is proportional to the block proportion (the largest block of each type of nodes having the same size), and the connectivity between two blocks is an edge whose width and color grow with the connectivity, with the colors of the graphon. The connectivity within a block is drawn as a loop. Edges are curved arrows for directed networks. The list of parameters plotOptions for this mesoscopic plot is:

"seed":

seed to control the layout (free layout). Default value is NULL

"title":

character string for the title. Default value is NULL

"layout":

"free" (force-directed: the blocks are placed according to their connectivities), "groups" (one line of blocks per type of nodes, for bipartite SBM) or a matrix with the coordinates of the blocks (one row per block, rows then columns for the bipartite SBM). Default value is NULL: "free" for simple SBM, "groups" for bipartite SBM

"vertex.color":

Color of the blocks, one per type of nodes. Default values are taken in a hue palette without the reds of the connectivities

"vertex.frame.color":

Color of the border of the blocks. Default value is NA (no border)

"vertex.shape":

"circle", "square", "diamond" or "triangle", one per type of nodes. Default value is "circle": the types of nodes are distinguished by their colors

"vertex.size":

Factor multiplying the size of the blocks, one per type of nodes. Default value is 1

"vertex.label.name":

Prefix of the labels of the blocks, one per type of nodes. Default value is NULL: the number of the block for a simple SBM, the shortest prefixes of the labels of the dimensions which distinguish them for a bipartite SBM

"vertex.label.color":

Default value is "black"

"vertex.label.size":

Size of the labels. Default value is 3.5

"vertex.label.inside":

The label of a block is drawn inside it when its radius is at least this fraction of the radius of the largest block (for a label of 2 characters, the fraction being proportional to the number of characters), outside it otherwise. Default value is 0.5. Set it to 0 to draw all the labels inside the blocks

"withinBlock":

Representation of the connectivity within the blocks for simple SBM: "loop" (a loop, as the other connections) or "fill" (the color of the block). Default value is "loop"

"edge.threshold":

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

"edge.width":

Factor multiplying the width of the edges. Default value is 1

"edge.curved":

Curvature of the edges for directed networks. Default value is 0.2

"edge.arrow.size":

Factor multiplying the size of the arrows for directed networks. Default value is 1

"block.color", "blockAlpha.min", "blockAlpha.max", "limits":

Colors of the connectivities, as for the graphon (see below)

For multipartite SBM, the list of parameters plotOptions for the mesoscopic plot (drawn with ggplot2, the free layout being computed with igraph) is:

"seed":

seed to control the free layout. Default value is NULL

"title":

character string for the title. Default value is NULL

"layout":

"free" (the blocks are placed according to their connectivities, whatever their functional group), "groups" (one row of blocks per functional group) or a matrix with the coordinates of the blocks (one row per block, in the order of the functional groups). Default value is "free"

"vertex.color":

Colors of the functional groups. Default values are taken in a hue palette without the reds of the connectivities

"vertex.frame.color":

Color of the border of the blocks. Default value is NA (no border)

"vertex.shape":

"circle", "square", "diamond" or "triangle", one per functional group. Default value is "circle": the functional groups are distinguished by their colors

"vertex.size":

Size of the node (default is 1)

"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

"vertex.label.inside":

The label of a block is drawn inside it when its radius is at least this fraction of the radius of the largest block (for a label of 2 characters, the fraction being proportional to the number of characters), outside it otherwise. Default value is 0.5

"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 1

"edge.arrow.size":

Default value is 1

"edge.arrow.width":

Default value is 1

"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

"names.size":

Numeric. Size (in pts) of the row and column names. Default value is NULL: the size decreases with the number of nodes, so that the names do not overlap on a 5 inches plot

"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

"blockBackground":

Boolean. Color the background of each block (when ordered = TRUE), with an opacity growing with the mean value of the entries in the block. Default value is TRUE for type = 'data' and FALSE for type = 'expected'

"graphonColors":

Boolean. Color the entries with the colors of the graphon (see below) instead of gray levels. Default value is TRUE for type = 'expected' and FALSE for type = 'data'

"block.color":

Chain of character. The color of the block background. Default value is red

"blockAlpha.min", "blockAlpha.max":

Numeric. Opacity of the least and most dense blocks. Default values are 0.1 and 0.6

For type = 'graphon', the blocks are drawn with the colors of the block background of the data plot. The axes are in number of nodes, so that the aspect ratio of the plot reflects the dimensions of the network. The list of parameters plotOptions is

"legend", "legend.title", "legend.position", "title", "line.color", "line.width":

As for the 'data' plot

"block.color", "blockAlpha.min", "blockAlpha.max":

As for the 'data' plot

"limits":

Numeric vector of length 2. Range of the connectivity values mapped to the colors. Default value is NULL: from 0 to the maximal value (or the range for negative values). Set it to compare several graphons on the same color scale, for instance c(0, 1) for Bernoulli models

The graphon is drawn from the connectivity parameters only, without the effect of the covariates.

Value

a ggplot2 object for the 'data', 'expected' and 'graphon', and 'meso'. For 'meso', the coordinates of the blocks are in the attribute "blockLayout" of the plot (a matrix with one row per block, named by the labels of the blocks): they can be modified and given back in plotOptions$layout, for instance lay <- attr(plot(mySBM, type = "meso"), "blockLayout"), then lay["P1", ] <- c(0, 2) and plot(mySBM, type = "meso", plotOptions = list(layout = lay))

Description

Plot an alluvial plot between clusterings

Usage

plotAlluvial(listMemberships, plotOptions = list())

Arguments

Details

The list of parameters plotOptions provides the following options

• "curvy" numeric, controls the curvature of the alluvial. Default value = 0.3

• "alpha numeric, vector of transparency of the stripes. Default value = 0.8

• "gap.width" numeric, relative width of inter-category gaps. Default value = 0.1

• "col" vector of colors of the stripes. Default value is NULL: the stripes are colored according to the clusters of the first clustering

• "border" vector of border colors for the stripes. Default is white

• "reorder" boolean. If TRUE, the clusters of each clustering are stacked so as to follow the clusters of the previous one, which limits the crossings of the stripes. The labels of the clusters are not changed. Default value = TRUE

Value

display the alluvial plot, returns invisibly a list with the plotOptions and the table of frequencies

Examples

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

Description

Draws the block connectivity of a simple or bipartite SBM on the unit square, each block being sized by its proportion. The axes are in number of nodes, so that the aspect ratio of the plot reflects the dimensions of the network.

Usage

plotMyGraphon(
  connectParam,
  blockProp,
  nbNodes = 1,
  dimLabels = c(row = "row", col = "col"),
  plotOptions = list()
)

Arguments

Details

The graphon of an SBM is the piecewise constant function on $[0,1]^2$ whose value on the rectangle of row block $k$ and column block $q$ is the connectivity parameter $\alpha_{kq}$; the sides of the rectangle are the proportions $\pi_k$ and $\pi_q$ of the blocks. Contrary to the matrix plots (type = 'data' or 'expected' in plot.SBM), it does not depend on the nodes nor on their memberships, only on the parameters of the model.

The blocks are drawn with the colors of the block background of the matrix plot (plotMyMatrix), so that both plots can be put side by side. For an SBM object (sampled or estimated), plot(x, type = 'graphon') gives the same plot.

The list of parameters plotOptions for the graphon plot 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'

• "line.color": Chain of character. The color of the lines to separate blocks. Default value is red

• "line.width": Numeric. Width of the lines to separate blocks. Default value is NULL, automatically chosen

• "title": Chain of character. Title of the plot. Default value is NULL

• "block.color": Chain of character. The color of the blocks. Default value is red

• "blockAlpha.min", "blockAlpha.max": Numeric. Opacity of the blocks with the lowest and highest connectivity. Default values are 0.1 and 0.6

• "limits": Numeric vector of length 2. Range of the connectivity values mapped to the colors. Default value is NULL: from 0 to the maximal value (or the range for negative values). Set it to compare several graphons on the same color scale, for instance c(0, 1) for Bernoulli models

Value

a ggplot object corresponding to the plot

See Also

plot.SBM, plotMyMatrix

Examples

## simple SBM
plotMyGraphon(matrix(c(0.8, 0.1, 0.1, 0.4), 2, 2), blockProp = c(0.3, 0.7),
              nbNodes = 50, dimLabels = 'individuals')
## bipartite SBM
plotMyGraphon(matrix(c(0.7, 0.4, 0.1, 0.4, 0.15, 0.03), 2, 3, byrow = TRUE),
              blockProp = list(row = c(0.2, 0.8), col = c(0.1, 0.3, 0.6)),
              nbNodes = c(90, 120), dimLabels = c(row = 'Pollinators', col = 'Plants'),
              plotOptions = list(legend = TRUE, limits = c(0, 1)))
## from an SBM object: the parameters of a sampled network
mySampler <- sampleSimpleSBM(nbNodes = 60, blockProp = c(0.5, 0.5),
                             connectParam = list(mean = matrix(c(0.6, 0.1, 0.1, 0.3), 2, 2)))
plotMyGraphon(mySampler$connectParam, mySampler$blockProp, mySampler$nbNodes,
              dimLabels = 'node', plotOptions = list(title = 'Graphon'))
## same plot
plot(mySampler, type = 'graphon')

Description

Plot an adjacency or incidence Matrix

Usage

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

Arguments

Details

The list of parameters plotOptions for the matrix plot 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

• "names.size": Numeric. Size (in pts) of the row and column names. Default value is NULL: the size decreases with the number of nodes, so that the names do not overlap on a 5 inches plot

• "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

• "blockBackground": Boolean. Color the background of each block, with an opacity growing with the mean value of the entries in the block. Only used when a clustering is provided. Default value is TRUE

• "block.color": Chain of character. The color of the block background. Default value is red

• "blockAlpha.min", "blockAlpha.max": Numeric. Opacity of the least and most dense blocks. Default values are 0.1 and 0.6

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))

Description

Plot the matrices corresponding to a Multipartite Network

Usage

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

Arguments

Details

plotOptions is a list containing the following items

• "normalized": Boolean. TRUE if the various matrices are presented in the same scale (between O and 1). FALSE otherwise. Default value FALSE

• "compact": Boolean. Default value is TRUE if you ask for the matrices to be transposed to have a more compact view

• "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'

• "nodeNames": Set true if the node Names must be plotted. Default value is FALSE

• "line.color": The color of the lines to separate groups. Default value is red

• "line.width": Width of the lines to separate groups. Default value is NULL, automatically chosen

• "title": Title of the plot. Default value is NULL

• "names.size": Numeric. Size (in pts) of the node names. Default value is NULL: the size decreases with the number of nodes

• "blockBackground": Boolean. Color the background of each block, with an opacity growing with the mean value of the entries in the block. Only used when a clustering is provided. Default value is TRUE

• "graphonColors": Boolean. Color the entries with the colors of the graphon (from blockAlpha.min to blockAlpha.max opacity of block.color) instead of white to black. Ignored for binary matrices. Default value is FALSE

• "block.color": Chain of character. The color of the block background. Default value is red

• "blockAlpha.min", "blockAlpha.max": Numeric. Opacity of the least and most dense blocks. Default values are 0.1 and 0.6

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))

Description

Plot the matrices corresponding to a Multiplex Network

Usage

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

Arguments

Details

plotOptions is a list containing the following items

• "normalized": Boolean. TRUE if the various matrices are presented in the same scale (between O and 1). FALSE otherwise. Default value FALSE

• "compact": Boolean. Default value is TRUE if you ask for the matrices to be transposed to have a more compact view

• "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'

• "nodeNames": Set true if the node Names must be plotted. Default value is FALSE

• "line.color": The color of the lines to separate groups. Default value is red

• "line.width": Width of the lines to separate groups. Default value is NULL, automatically chosen

• "title": Title of the plot. Default value is NULL

• "names.size": Numeric. Size (in pts) of the node names. Default value is NULL: the size decreases with the number of nodes

• "blockBackground": Boolean. Color the background of each block, with an opacity growing with the mean value of the entries in the block. Only used when a clustering is provided. Default value is TRUE

• "graphonColors": Boolean. Color the entries with the colors of the graphon (from blockAlpha.min to blockAlpha.max opacity of block.color) instead of white to black. Ignored for binary matrices. Default value is FALSE

• "block.color": Chain of character. The color of the block background. Default value is red

• "blockAlpha.min", "blockAlpha.max": Numeric. Opacity of the least and most dense blocks. Default values are 0.1 and 0.6

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))

Description

Make predictions from an SBM.

Usage

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

Arguments

Value

a matrix of expected values for each dyad

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 = vector("list", 2),
  connectParam,
  model = "bernoulli",
  dimLabels = c(row = "row", col = "col"),
  covariates = list(),
  covariatesParam = numeric(0),
  nodesCovariates = vector("list", 2),
  nodesCovariatesParam = vector("list", 2)
)

Arguments

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)

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

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))

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

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

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 = numeric(0),
  connectParam,
  model = "bernoulli",
  directed = FALSE,
  dimLabels = c("node"),
  covariates = list(),
  covariatesParam = numeric(0),
  nodesCovariates = matrix(0, 0, 0),
  nodesCovariatesParam = matrix(0, 0, 0)
)

Arguments

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)

Description

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

Active bindings

Methods

Public methods

• SBM$new()

• SBM$rNetwork()

• SBM$show()

• SBM$print()

• SBM$clone()

SBM$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(),
  nodesCovarList = list(),
  nodesCovarParam = list()
)

Arguments

SBM$rNetwork()

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

Usage

SBM$rNetwork(store = FALSE)

Arguments

Returns

a list with the sampled block and network

SBM$show()

print method

Usage

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

Arguments

SBM$print()

print method

Usage

SBM$print()

SBM$clone()

The objects of this class are cloneable with this method.

Usage

SBM$clone(deep = FALSE)

Arguments

Description

R6 class for Simple SBM

Super class

SBM -> SimpleSBM

Active bindings

Methods

Public methods

• SimpleSBM$new()

• SimpleSBM$rMemberships()

• SimpleSBM$rEdges()

• SimpleSBM$predict()

• SimpleSBM$show()

• SimpleSBM$plot()

• SimpleSBM$clone()

SimpleSBM$new()

constructor for SBM

Usage

SimpleSBM$new(
  model,
  nbNodes,
  directed,
  blockProp,
  connectParam,
  dimLabels = c("node"),
  covarParam = numeric(length(covarList)),
  covarList = list(),
  nodesCovarList = list(node = matrix(0, 0, 0)),
  nodesCovarParam = list(node = matrix(0, 0, 0))
)

Arguments

SimpleSBM$rMemberships()

a method to sample new block memberships for the current SBM

Usage

SimpleSBM$rMemberships(store = FALSE)

Arguments

Returns

the sampled blocks

SimpleSBM$rEdges()

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

Usage

SimpleSBM$rEdges(store = FALSE)

Arguments

Returns

the sampled network

SimpleSBM$predict()

prediction under the currently parameters

Usage

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

Arguments

Returns

a matrix of expected values for each dyad

SimpleSBM$show()

show method

Usage

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

Arguments

SimpleSBM$plot()

basic matrix plot method for SimpleSBM object or mesoscopic plot

Usage

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

Arguments

Returns

a ggplot2 object

SimpleSBM$clone()

The objects of this class are cloneable with this method.

Usage

SimpleSBM$clone(deep = FALSE)

Arguments

Description

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

Details

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

• "nbCores integer for number of cores used. Default is 2 (1 under Positron, which does not allow forking)

• "verbosity" integer for verbosity (0, 1). Default is 1

• "plot" boolean, should the ICL be dynamically plotted or not. Default is TRUE, FALSE when "verbosity" is 0

• "exploreFactor" control the exploration of the number of groups

• "exploreMin" explore at least until exploreMin even if the exploration factor rule is achieved. Default 4. See the package blockmodels for details.

• "exploreMax" Stop exploration at exploreMax even if the exploration factor rule is not achieved. Default Inf. See the package blockmodels for details.

• "nbBlocksRange" minimal and maximal number or blocks explored

• "fast" logical: should approximation be used for Bernoulli model with covariates. Default to TRUE

Super classes

SBM -> SimpleSBM -> SimpleSBM_fit

Active bindings

Methods

Public methods

• SimpleSBM_fit$new()

• SimpleSBM_fit$optimize()

• SimpleSBM_fit$setModel()

• SimpleSBM_fit$reorder()

• SimpleSBM_fit$show()

• SimpleSBM_fit$clone()

SimpleSBM_fit$new()

constructor for a Simple SBM fit

Usage

SimpleSBM_fit$new(
  adjacencyMatrix,
  model,
  directed,
  dimLabels = c(node = "nodeName"),
  covarList = list(),
  nodesCovarList = list(matrix(nrow = 0, ncol = 0))
)

Arguments

SimpleSBM_fit$optimize()

function to perform optimization

Usage

SimpleSBM_fit$optimize(estimOptions = list())

Arguments

SimpleSBM_fit$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

SimpleSBM_fit$reorder()

permute group labels by order of decreasing probability

Usage

SimpleSBM_fit$reorder()

SimpleSBM_fit$show()

show method

Usage

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

Arguments

SimpleSBM_fit$clone()

The objects of this class are cloneable with this method.

Usage

SimpleSBM_fit$clone(deep = FALSE)

Arguments

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)