knitr::opts_chunk$set( collapse = TRUE, comment = "#>", message=FALSE, warning=FALSE )
This vignette describes the two implemented methods for blockmodeling in signed networks.
library(igraph) library(signnet)
In signed blockmodeling, the goal is to determine k
blocks of nodes such that all intra-block edges
are positive and inter-block edges are negative. In the example below, we construct a network with a perfect
block structure with sample_islands_signed()
. The network consists of 10 blocks with 10 vertices each, where each block
has a density of 1 (of positive edges). The function signed_blockmodel()
is used to construct the blockmodel.
The parameter k
is the number of desired blocks. alpha
is a trade-off parameter. The function minimizes $P(C)=\alpha N+(1-\alpha)P$, where $N$ is the total number of negative ties within blocks and $P$ be the total number of positive ties between blocks.
g <- sample_islands_signed(10,10,1,20) clu <- signed_blockmodel(g,k = 10,alpha = 0.5) table(clu$membership) clu$criterion
The function returns a list with two entries. The block membership of nodes and the value of $P(C)$.
The function ggblock()
can be used to plot the outcome of the blockmodel (ggplot2
is required).
ggblock(g,clu$membership,show_blocks = TRUE)
knitr::include_graphics("blockmodel_example.png")
If the parameter annealing
is set to TRUE, simulated annealing is used in the optimization step.
This generally leads to better results but longer runtimes.
data("tribes") set.seed(44) #for reproducibility signed_blockmodel(tribes,k = 3,alpha=0.5,annealing = TRUE) signed_blockmodel(tribes,k = 3,alpha=0.5,annealing = FALSE)
The function signed_blockmodel()
is only able to provide a blockmodel where the diagonal blocks are positive and
off-diagonal blocks are negative. The function signed_blockmodel_general()
can be used to specify different block structures.
In the below example, we construct a network that contains three blocks. Two have positive and one has negative intra-group ties.
The inter-group edges are negative between group one and two, and one and three. Between group two and three, all edges are positive.
g1 <- g2 <- g3 <- graph.full(5) V(g1)$name <- as.character(1:5) V(g2)$name <- as.character(6:10) V(g3)$name <- as.character(11:15) g <- Reduce("%u%",list(g1,g2,g3)) E(g)$sign <- 1 E(g)$sign[1:10] <- -1 g <- add.edges(g,c(rbind(1:5,6:10)),attr = list(sign=-1)) g <- add.edges(g,c(rbind(1:5,11:15)),attr = list(sign=-1)) g <- add.edges(g,c(rbind(11:15,6:10)),attr = list(sign=1))
The parameter blockmat
is used to specify the desired block structure.
set.seed(424) #for reproducibility blockmat <- matrix(c(1,-1,-1,-1,1,1,-1,1,-1),3,3,byrow = TRUE) blockmat general <- signed_blockmodel_general(g,blockmat,alpha = 0.5) traditional <- signed_blockmodel(g,k = 3,alpha = 0.5,annealing = TRUE) c(general$criterion,traditional$criterion)
knitr::include_graphics("blockmodel_general.png")
Doreian, Patrick, and Andrej Mrvar. 1996. "A Partitioning Approach to Structural Balance." Social Networks 18 (2): 149–68.
Doreian, Patrick, and Andrej Mrvar. 2009. "Partitioning Signed Social Networks." Social Networks 31 (1): 1–11.
Doreian, Patrick, and Andrej Mrvar. 2015. "Structural Balance and Signed International Relations." Journal of Social Structure 16: 1.
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