sampleMultiplexSBM {sbm}

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