Construct an adjency matrix from a matrix that represents a graph with R

Create a data frame with one row per entry of the matrix and the corresponding row and column number and then subset that data frame down to the entries that are 1. (@Andrew Gustar deleted his post but that post shows that the row and col columns of d could also have been expressed as d <- as.data.frame(which(m == 1, arr.ind = TRUE)) ). Now use outer to determine whether two rows of that data frame represent adjacent nodes or not. Change the ==1 to <=1 in the line that sets adj if nodes can be adjacent to themselves.

d <- data.frame(value = c(m), row = c(row(m)), col = c(col(m))) |>
  subset(value == 1)
adj <- +with(d, abs(outer(row, row, `-`)) + abs(outer(col, col, `-`)) == 1)

We can view the adjacency matrix easily by converting it to a sparse matrix.

Matrix::Matrix(adj)

giving:

23 x 23 sparse Matrix of class "dsCMatrix"   
                                            
 [1,] . 1 . . . . . . . . . . . . . . . . . . . . .
 [2,] 1 . 1 . 1 . . . . . . . . . . . . . . . . . .
 [3,] . 1 . . . . . . . . . . . . . . . . . . . . .
 [4,] . . . . . . 1 . . . . . . . . . . . . . . . .
 [5,] . 1 . . . . . . 1 . . . . . . . . . . . . . .
 [6,] . . . . . . 1 . . . 1 . . . . . . . . . . . .
 [7,] . . . 1 . 1 . . . . . . . . . . . . . . . . .
 [8,] . . . . . . . . 1 . . . . . . . . . . . . . .
 [9,] . . . . 1 . . 1 . 1 . . . . . . . . . . . . .
[10,] . . . . . . . . 1 . . 1 . . . . . . . . . . .
[11,] . . . . . 1 . . . . . . . 1 . . . . . . . . .
[12,] . . . . . . . . . 1 . . 1 . . . 1 . . . . . .
[13,] . . . . . . . . . . . 1 . 1 . . . . . . . . .
[14,] . . . . . . . . . . 1 . 1 . 1 . . . . . . . .
[15,] . . . . . . . . . . . . . 1 . . . 1 . . . . .
[16,] . . . . . . . . . . . . . . . . . . 1 . . . .
[17,] . . . . . . . . . . . 1 . . . . . . . . 1 . .
[18,] . . . . . . . . . . . . . . 1 . . . . . . . 1
[19,] . . . . . . . . . . . . . . . 1 . . . 1 . . .
[20,] . . . . . . . . . . . . . . . . . . 1 . 1 . .
[21,] . . . . . . . . . . . . . . . . 1 . . 1 . . .
[22,] . . . . . . . . . . . . . . . . . . . . . . 1
[23,] . . . . . . . . . . . . . . . . . 1 . . . 1 .

We can use igraph to plot the graph:

library(igraph)

set.seed(123)
g <- graph.adjacency(adj, mode = "undirected")
plot(g, vertex.color = "white", vertex.size = 10, vertex.label.cex = 0.7)

Note

m <- structure(c(1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 
0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1), .Dim = c(6L, 
6L), .Dimnames = list(NULL, NULL))

We can try this

v <- c(row(m) * m + 1i * col(m) * m)[m > 0]
d <- +(abs(outer(v, v, `-`)) == 1)

which gives

> d
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
 [1,]    0    1    0    0    0    0    0    0    0     0     0     0     0
 [2,]    1    0    1    0    1    0    0    0    0     0     0     0     0
 [3,]    0    1    0    0    0    0    0    0    0     0     0     0     0
 [4,]    0    0    0    0    0    0    1    0    0     0     0     0     0
 [5,]    0    1    0    0    0    0    0    0    1     0     0     0     0
 [6,]    0    0    0    0    0    0    1    0    0     0     1     0     0
 [7,]    0    0    0    1    0    1    0    0    0     0     0     0     0
 [8,]    0    0    0    0    0    0    0    0    1     0     0     0     0
 [9,]    0    0    0    0    1    0    0    1    0     1     0     0     0
[10,]    0    0    0    0    0    0    0    0    1     0     0     1     0
[11,]    0    0    0    0    0    1    0    0    0     0     0     0     0
[12,]    0    0    0    0    0    0    0    0    0     1     0     0     1
[13,]    0    0    0    0    0    0    0    0    0     0     0     1     0
[14,]    0    0    0    0    0    0    0    0    0     0     1     0     1
[15,]    0    0    0    0    0    0    0    0    0     0     0     0     0
[16,]    0    0    0    0    0    0    0    0    0     0     0     0     0
[17,]    0    0    0    0    0    0    0    0    0     0     0     1     0
[18,]    0    0    0    0    0    0    0    0    0     0     0     0     0
[19,]    0    0    0    0    0    0    0    0    0     0     0     0     0
[20,]    0    0    0    0    0    0    0    0    0     0     0     0     0
[21,]    0    0    0    0    0    0    0    0    0     0     0     0     0
[22,]    0    0    0    0    0    0    0    0    0     0     0     0     0
[23,]    0    0    0    0    0    0    0    0    0     0     0     0     0
      [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23]
 [1,]     0     0     0     0     0     0     0     0     0     0
 [2,]     0     0     0     0     0     0     0     0     0     0
 [3,]     0     0     0     0     0     0     0     0     0     0
 [4,]     0     0     0     0     0     0     0     0     0     0
 [5,]     0     0     0     0     0     0     0     0     0     0
 [6,]     0     0     0     0     0     0     0     0     0     0
 [7,]     0     0     0     0     0     0     0     0     0     0
 [8,]     0     0     0     0     0     0     0     0     0     0
 [9,]     0     0     0     0     0     0     0     0     0     0
[10,]     0     0     0     0     0     0     0     0     0     0
[11,]     1     0     0     0     0     0     0     0     0     0
[12,]     0     0     0     1     0     0     0     0     0     0
[13,]     1     0     0     0     0     0     0     0     0     0
[14,]     0     1     0     0     0     0     0     0     0     0
[15,]     1     0     0     0     1     0     0     0     0     0
[16,]     0     0     0     0     0     1     0     0     0     0
[17,]     0     0     0     0     0     0     0     1     0     0
[18,]     0     1     0     0     0     0     0     0     0     1
[19,]     0     0     1     0     0     0     1     0     0     0
[20,]     0     0     0     0     0     1     0     1     0     0
[21,]     0     0     0     1     0     0     1     0     0     0
[22,]     0     0     0     0     0     0     0     0     0     1
[23,]     0     0     0     0     1     0     0     0     1     0