The relationship is expressed as a matrix x like this:
A B C D
A 0 2 1 1
B 2 0 1 0
C 1 1 0 1
D 1 0 1 0
The entries refer to the number of connections they have.
Could anyone show me how to write it as an edge list?
I would prefer to write it as an edge list:
A B
A B
A C
A D
B C
But would this edge list allow me to create a network plot?
Using the igraph package:
x <- matrix(c(0,2,1,1,2,0,1,0,1,1,0,1,1,0,1,0), 4, 4)
rownames(x) <- colnames(x) <- LETTERS[1:4]
library(igraph)
g <- graph.adjacency(x)
get.edgelist(g)
# [,1] [,2]
# [1,] "A" "B"
# [2,] "A" "B"
# [3,] "A" "C"
# [4,] "A" "D"
# [5,] "B" "A"
# [6,] "B" "A"
# [7,] "B" "C"
# [8,] "C" "A"
# [9,] "C" "B"
# [10,] "C" "D"
# [11,] "D" "A"
# [12,] "D" "C"
I would also recommend you spend some time reading the igraph documentation at http://igraph.sourceforge.net/index.html since a lot of your recent questions are all simple case usages.
(As a bonus, plot(g) will answer your other question How to plot relationships in R?)