# Function that performs stochastic one-mode and linked blockmodeling by optimizing a single partition. If `clu` is a list, the method for linked/multilevel networks is applied ```r stochBlock( M, clu, weights = NULL, uWeights = NULL, diagonal = c("ignore", "seperate", "same"), limitType = c("none", "inside", "outside"), limits = NULL, weightClusterSize = 1, addOne = TRUE, eps = 0.001 ) ``` ## Arguments - `M`: A matrix representing the (usually valued) network. For multi-relational networks, this should be an array with the third dimension representing the relation. - `clu`: A partition. Each unique value represents one cluster. If the network is one-mode, than this should be a vector, else a list of vectors, one for each mode. Similarly, if units are comprised of several sets, clu should be the list containing one vector for each set. - `weights`: The weights for each cell in the matrix/array. A matrix or an array with the same dimensions as `M`. - `uWeights`: The weights for each unin. A vector with the length equal to the number of units (in all sets). - `diagonal`: How should the diagonal values be treated. Possible values are: * ignore - diagonal values are ignored * seperate - diagonal values are treated seperately * same - diagonal values are treated the same as all other values - `limitType`: Type of limit to use. Forced to 'none' if `limits` is `NULL`. Otherwise, one of either `outer` or `inner`. - `limits`: If `diagonal` is `"ignore"` or `"same"`, an array with dimensions equal to: * number of clusters (of all types) * number of clusters (of all types) * number of relations * 2 - the first is lower limit and the second is upper limit If `diagonal` is `"seperate"`, a list of two array. The first should be as described above, representing limits for off diagonal values. The second should be similar with only 3 dimensions, as one of the first two must be omitted. - `weightClusterSize`: The weight given to cluster sizes (logprobabilites) compared to ties in loglikelihood. Defaults to 1, which is "classical" stochastic blockmodeling. - `addOne`: Should one tie with the value of the tie equal to the density of the superBlock be added to each block to prevent block means equal to 0 or 1 and also "shrink" the block means toward the superBlock mean. Defaults to TRUE. - `eps`: If addOne = FALSE, the minimal deviation from 0 or 1 that the block mean/density can take. ## Returns A list of class `opt.par` normally passed other commands with `StockBlockORP` and containing: - **clu**: A vector (a list for multi-mode networks) indicating the cluster to which each unit belongs; - **IM**: Image matrix of this partition; - **weights**: The weights for each cell in the matrix/array. A matrix or an array with the same dimensions as `M`. - **uWeights**: The weights for each unit. A vector with the length equal to the number of units (in all sets). - **err**: - weighted log-likelihood. - **ICL**: Integrated Criterion Likelihood for this partition ## Examples ```r # Create a synthetic network matrix set.seed(2022) library(blockmodeling) k<-2 # number of blocks to generate blockSizes<-rep(20,k) IM<-matrix(c(0.8,.4,0.2,0.8), nrow=2) clu<-rep(1:k, times=blockSizes) n<-length(clu) M<-matrix(rbinom(n*n,1,IM[clu,clu]),ncol=n, nrow=n) clu<-sample(1:2,nrow(M),replace=TRUE) plotMat(M,clu) # Have a look at this random partition res<-stochBlock(M,clu) # Optimising the partition plot(res) # Have a look at the optimised parition # Create a synthetic linked-network matrix set.seed(2022) library(blockmodeling) IM<-matrix(c(0.8,.4,0.2,0.8), nrow=2) clu<-rep(1:2, each=20) # Partition to generate n<-length(clu) nClu<-length(unique(clu)) # Number of clusters to generate M1<-matrix(rbinom(n^2,1,IM[clu,clu]),ncol=n, nrow=n) # First network M2<-matrix(rbinom(n^2,1,IM[clu,clu]),ncol=n, nrow=n) # Second network M12<-diag(n) # Linking network nn<-c(n,n) k<-c(2,2) Ml<-matrix(0, nrow=sum(nn),ncol=sum(nn)) Ml[1:n,1:n]<-M1 Ml[n+1:n,n+1:n]<-M2 Ml[n+1:n, 1:n]<-M12 plotMat(Ml) # Linked network clu1<-sample(1:2,nrow(M1),replace=TRUE) clu2<-sample(3:4,nrow(M1),replace=TRUE) plotMat(Ml,list(clu1,clu2)) # Have a look at this random partition res<-stochBlock(Ml,list(clu1,clu2)) # Optimising the partition plot(res) # Have a look at the optimised parition ``` ## References Škulj, D., & Žiberna, A. (2022). Stochastic blockmodeling of linked networks. Social Networks, 70, 240-252, tools:::Rd_expr_doi("10.1371/journal.pcbi.1005697") . ## See Also `stochBlockORP` ## Author(s)

stochBlock function