Mapping edgelists to an adjacency matrix (and sum them together)

Question

I want to map a number of (undirected) friendship networks (in edgelist format) to an adjacency matrix consisting of all possible nodes (i.e., persons) using R. To begin with, I construct a smaller 4-person circle x <- c(1, 2, 3, 4) which consists of 6 unique edges (1-2, 1-3, 1-4, 2-3, 2-4, 3-4). I then collapsed this set of 6 unique edges into a single list, such that it can be converted into a symmetric matrix using igraph applications (see below).

x = c(1,2,3,4)
x_pairs = combn(x, 2)
List <- split(x_pairs, rep(1:ncol(x_pairs), each = nrow(x_pairs)))
library(purrr)
new_list <- purrr::flatten(List)
g <- make_graph(unlist(new_list), directed = F)
m <- as_adjacency_matrix(g, sparse = F)
m

     [,1] [,2] [,3] [,4]
[1,]    0    1    1    1
[2,]    1    0    1    1
[3,]    1    1    0    1
[4,]    1    1    1    0

My dataset has more than one of such smaller friendship circles consist of members out of a total of 50 persons and the memberships of these circles may or may not overlap. So my question is how do I map a series of smaller matrix values like the m above to a 50 by 50 adjacency matrix in two different ways:

(1) without repeating: say, if 3 and 4 are friends in one circle but they are also linked in another circle, the edge between 3 and 4 should remain 1 (but not add up to 2) (2) cumulatively: if relationship in multiple circles indicates stronger friendship, then it might be more informative to map these circles into a weighted adjacency matrix where each cell in the matrix represents the cumulative counts of row and column id's friendship in different circles. In 3 and 4's situation, their edge value should be 1 + 1 = 2.

I've checked out this and other previous threads but can't seem to figure out how to do this, it will be really appreciated if someone could enlighten me on this.

Answer 1

There are various ways to achieve it. It looks like doing it in graph theoretical terms in igraph is a little more tedious than dealing directly with adjacency matrices. Let

circles <- list(1:3, 2:4) # Friendship circles with identities 1, ..., n
n <- max(unlist(circles)) # Total number of people
nM <- matrix(0, n, n) # n x n matrix of zeroes

Then

adjs <- lapply(circles, function(cr) {nM[cr, cr] <- 1; nM[cbind(cr, cr)] <- 0; nM})

is a list of n x n adjacency matrices for each friendship circle (mostly zeroes in each case).

Then the two types of aggregate matrices can be obtained by

(adj1 <- Reduce(`+`, adjs))
#      [,1] [,2] [,3] [,4]
# [1,]    0    1    1    0
# [2,]    1    0    2    1
# [3,]    1    2    0    1
# [4,]    0    1    1    0
(adj2 <- 1 * (adj1 > 0))
#      [,1] [,2] [,3] [,4]
# [1,]    0    1    1    0
# [2,]    1    0    1    1
# [3,]    1    1    0    1
# [4,]    0    1    1    0