sampleMultiplexSBM function

Sampling of Multiplex SBMs

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

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.

Returns

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