Just adding knowledge to this old question:

I have a tutorial here on Biostars in which I do this via igraph: Network plot from expression data in R using igraph

library(igraph)

#Create a graph adjacency based on correlation distances between genes in  pairwise fashion.
g <- graph.adjacency(
  as.matrix(as.dist(cor(t(estrogenMainEffects), method="pearson"))),
  mode="undirected",
  weighted=TRUE,
  diag=FALSE
)

Hello!

An example with a matrix 5x5:

M <- matrix(rnorm(25), nrow=5)
colnames(M) <- letters[1:5]
rownames(M) <- letters[1:5]
edges <- NULL
for (i in 1:nrow(M)) {
    for (j in 1:ncol(M)) {
        edges <- rbind(edges, c(rownames(M)[i], rownames(M)[j], M[i,j]))
    }
}

colnames(edges) <- c('node1', 'node2', 'value')
write.table(edges, 'edges.txt', row.names=FALSE, quote=FALSE, sep='\t')

After this, it is possible to use Cytoscape to load 'edges.txt' and its filters to remove the edges according to a threshold.

I guess you'll be using the distance between the nodes as edge weights. In that case you can filter edges based on their weights which in this case is the distance.