Indicating the same clusters by colour between two Igraph plots using k mean clustering

Question

I have two adjacency matrices from two different datasets with the same variables:

Amat <- read.table(text = "
    Si  N1  N2  A1  A2  A3  A4  A5  Z1  Z2  Z3  Z5
Si 367   0   0  48   0 365   0   0   0   0   0   0
N1   0 368   0 368 275  58 365 360   0   0   0   0
N2   0   0 368   1 368   0   1   8   0   0   0   3
A1  37 272   0 103   0   8   0   0  18 351   0   2
A2   0 151 361   0   3   0   0   1   0   0 353  46
A3 269  49   0  39   0 116   0   0 345   9   0   0
A4   0 306   1   0   0   0 211  60   0   0   0   1
A5   0 215   8   0   0   0 145 248   0   0   0  10
Z1   0   0   0  17   0 351   0   0 355 240   1   3
Z2   0   0   0 350   0   9   0   0 201 213 211 175
Z3   0   0   0   0 362   0   0   0   1 195 103  11
Z5   0   0   3   2  45   0   1  10   3 177  12 348
", header = TRUE)

and

Amat2 <- read.table(text = "
    Si  N1  N2  A1  A2  A3  A4  A5  Z1  Z2  Z3  Z5
Si 639   0   0  89   0 637   0   0   0   0   0   0
N1   0 640   0 639 487 111 637 632   0   0   0   0
N2   0   0 640   1 639   0   1   8   0   0   0   7
A1  77 514   0 138   0  12   0   0  35 614   0   4
A2   0 281 632   0   3   0   0   1   1   1 609  70
A3 469  98   0  70   0 198   0   0 597  16   0   0
A4   0 529   1   0   0   0 406 110   0   0   0   1
A5   0 419   8   0   0   0 219 424   0   0   0  12
Z1   0   0   0  34   1 609   0   0 623 409   1   7
Z2   0   0   0 614   1  16   0   0 311 321 334 323
Z3   0   0   0   0 626   0   0   0   1 347 198  37
Z5   0   0   7   4  70   0   1  12   7 325  38 603
", header = TRUE)

I have conducted a clustering algorithm on both and successfully plotted the edge-and-vertices igraphs:

library(igraph)
library(stats)
Amat <- as.matrix(Amat)
Amat2 <- as.matrix(Amat2)

#clustering dataset 1
Lmat <- diag(rowSums(Amat)) - Amat #laplacian matrix
D_half <- diag(sqrt(1/rowSums(Amat)))
normL <- D_half %*% Lmat %*% D_half #normalize laplacian
laplacian_eigen <- eigen(normL)
sorted_eigenvectors <- laplacian_eigen$vectors[, order(laplacian_eigen$values)]

# K-means clustering
library(stats)
kmeans_result <- kmeans(sorted_eigenvectors[, 1:8], centers = 8)


#clustering dataset 2
Lmat2 <- diag(rowSums(Amat2)) - Amat2 #laplacian matrix
D_half2 <- diag(sqrt(1/rowSums(Amat2)))
normL2 <- D_half2 %*% Lmat2 %*% D_half2 #normalize laplacian
laplacian_eigen2 <- eigen(normL2)
sorted_eigenvectors2 <- laplacian_eigen2$vectors[, order(laplacian_eigen2$values)]

kmeans_result2 <- kmeans(sorted_eigenvectors2[, 1:8], centers = 8)

############### plotting ##########################

# Create an igraph graph object from the adjacency matrix
graph1 <- graph_from_adjacency_matrix(Amat, mode = "undirected")
graph2 <- graph_from_adjacency_matrix(Amat2, mode = "undirected")

par(mfrow=c(1,2))
plot(graph1, vertex.color = kmeans_result$cluster, main = 'set1') #multi-plot
plot(graph2, vertex.color = kmeans_result2$cluster, main = 'set2')

but the problem is they are difficult to compare because of the colours:

In instances where clusters are the same in both sets, I would like them to be the same colour -- like in the example of Z1 and A3 that are clustered together in both datasets and are both green. So for instance N1 and A4 should be the same colour since they are both clustered together in both sets.

I've tried ordering my kmeans$clusters, but I didn't do it right and I don't want to mess up the cluster to variable assignments.

Answer 1

Set the vertex.color for both the same:

par(mfrow=c(1,2))
plot(graph1, vertex.color = kmeans_result$cluster, main = 'set1') #multi-plot
plot(graph2, vertex.color = kmeans_result$cluster, main = 'set2')