Detect bi-cliques in r for bipartite graph - r

Question

I am trying to recreate the Biclique Communities method (Lehmann, Schwartz, & Hansen, 2008) in R which relies on the definition of a Ka,b biclique. The example below shows two adjacent K2,2 bicliques - the first clique is {A,B,1,2} and the second clique is {B,C,2,3}. I would like to be able to identify these cliques using R so that I can apply this to a broader dataset.
I have included my attempt so far in R and I am stuck with the following two issues:
If I use the standard walktrap.community it recognises the communities but does not allow the set {B,2} to belong in both cliques
If I use an updated clique.community function this doesn't seem to identify the cliques or I don't understand correctly (or both)
Example code:
library(igraph)
clique.community <- function(graph, k) {
clq <- cliques(graph, min=k, max=k)
edges <- c()
for (i in seq_along(clq)) {
for (j in seq_along(clq)) {
if ( length(unique(c(clq[[i]], clq[[j]]))) == k+1 ) {
edges <- c(edges, c(i,j))
}
}
}
clq.graph <- simplify(graph(edges))
V(clq.graph)$name <- seq_len(vcount(clq.graph))
comps <- decompose.graph(clq.graph)
lapply(comps, function(x) {
unique(unlist(clq[ V(x)$name ]))
})
}
users <- c('A', 'A', 'B', 'B', 'B', 'C', 'C')
resources <- c(1, 2, 1, 2, 3, 2, 3)
cluster <- data.frame(users, resources)
matrix <- as.data.frame.matrix(table(cluster))
igraph <- graph.incidence(matrix)
clique.community(igraph, 2)
walktrap.community(igraph)

Answer 1

Beware that the above solution becomes inefficient very quickly even for small (dense) graphs and values of k,l due to the fact that comb <- combn(vMode1, k) becomes extremely large.
A more efficient solution can be found in the "biclique" package that is in development at https://github.com/YupingLu/biclique.

Answer 2

I managed to find a script for this in the Sisob workbench
computeBicliques <- function(graph, k, l) {
vMode1 <- c()
if (!is.null(V(graph)$type)) {
vMode1 <- which(!V(graph)$type)
vMode1 <- intersect(vMode1, which(degree(graph) >= l))
}
nb <- get.adjlist(graph)
bicliques <- list()
if (length(vMode1) >= k) {
comb <- combn(vMode1, k)
i <- 1
sapply(1:ncol(comb), function(c) {
commonNeighbours <- c()
isFirst <- TRUE
sapply(comb[,c], function(n) {
if (isFirst) {
isFirst <<- FALSE
commonNeighbours <<- nb[[n]]
} else {
commonNeighbours <<- intersect(commonNeighbours, nb[[n]])
}
})
if (length(commonNeighbours) >= l) {
bicliques[[i]] <<- list(m1=comb[,c], m2=commonNeighbours)
}
i <<- i + 1
})
}
bicliques
}