Manhattan Matrix by 2 Matrices is non symmetric but should be - r

Question

I created two matrices that have random integers as components, the dimension of the matrix doesn't matter. Then I want to calculate the distance matrix by the Manhattan method and frame it as a matrix. The matrix should be symmetric, but when I frame it as a matrix, the output is a non
symmetric distance matrix.
By that matrix (that should be the output) I want to calculate a cluster.
Where is my mistake?
Code:
a <- c(sample.int(30,6))
b <- c(sample.int(30,6))
c <- c(sample.int(30,6))
d <- c(sample.int(30,6))
e <- c(sample.int(30,6))
f <- c(sample.int(30,6))
V2 <- rbind(a,b,c,d,e,f)
V1 <- rbind(a,b,c,d,e,f)
d1MNR <- matrix(dist(Vorlage1,Vorlage2, method="manhattan")) #### Is non symmetric
d1MR <- matrix(dist(V1,V2,upper=TRUE, diag=TRUE ,method="manhattan")) #### Should be symmetric, but is not
d1MR ### Generate output
hclust <- hclust(dist(d1MR), method = "single") ### Clustering

Answer 1

You can make a symmetrical distance matrix from V1 or a symmetrical matrix from V2, but the only way to make a symmetric matrix from both of them together is to combine them V12 <- rbind(V1, V2). The dist() function returns a dist object that hclus can use. You do not need to convert them to a matrix. In your example V1 and V2 are identical. We need them to be different:
set.seed(42)
V1 <- matrix(sample.int(30, 36, replace=TRUE), 6)
V2 <- matrix(sample.int(30, 36, replace=TRUE), 6)
V12 <- rbind(V1, V2)
rownames(V12) <- paste(rep(c("V1", "V2"), each=6), 1:6, sep=":")
colnames(V12) <- letters[1:6]
V12
# a b c d e f
# V1:1 17 18 4 18 4 28
# V1:2 5 26 25 15 5 8
# V1:3 1 17 5 3 13 3
# V1:4 25 15 14 9 5 26
# V1:5 10 24 20 25 20 1
# V1:6 4 7 26 27 2 10
# V2:1 24 8 28 3 18 22
# V2:2 30 4 5 24 6 21
# V2:3 11 4 4 23 6 2
# V2:4 15 22 2 17 2 23
# V2:5 22 18 24 21 20 6
# V2:6 26 13 18 26 3 26
d1MNR <- dist(V12, method="manhattan")
hclust <- hclust(d1MNR, method = "single")
plot(hclust)
If you want to look at a symmetrical distance matrix:
print(d1MNR, upper=TRUE, diag=TRUE)
# V1:1 V1:2 V1:3 V1:4 V1:5 V1:6 V2:1 V2:2 V2:3 V2:4 V2:5 V2:6
# V1:1 0 65 67 33 79 75 76 43 53 16 66 39
# V1:2 65 0 58 66 44 38 79 90 64 57 49 72
# V1:3 67 58 0 72 62 76 79 88 52 67 69 98
# V1:4 33 66 72 0 86 78 45 46 74 43 63 26
# V1:5 79 44 62 86 0 58 83 90 54 73 31 72
# V1:6 75 38 76 78 58 0 75 68 48 73 59 54
# V2:1 76 79 79 45 83 75 0 67 93 80 52 59
# V2:2 43 90 88 46 90 68 67 0 40 49 73 36
# V2:3 53 64 52 74 54 48 93 40 0 55 65 68
# V2:4 16 57 67 43 73 73 80 49 55 0 72 49
# V2:5 66 49 69 63 31 59 52 73 65 72 0 57
# V2:6 39 72 98 26 72 54 59 36 68 49 57 0