Vfrdtyky

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.

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