Adjacency matrix clustering with constraints: maximum and minimum values for the sum of node weights

I need to find clusters based on the following adjacency matrix:

library(dplyr)

# importing the adjacency matrix
adj_matrix <- read.table('https://raw.githubusercontent.com/sergiocostafh/adjmatrix_example/main/adj_m.txt',header = T,check.names = F) %>% as.matrix()
row.names(adj_matrix) <- colnames(adj_matrix)

Using igraph package I turn the matrix into a graph to perform the clustering. The ggraph package helps with visualization.

library(ggplot2)
library(igraph)

# turning into a graph
grafo <- graph_from_adjacency_matrix(adj_matrix,'undirected')

# detecting clusters
fc <- cluster_walktrap(as.undirected(grafo))

# results to data.frame
ms <- data.frame(id=membership(fc)%>%names(),cluster=as.character(as.vector(membership(fc))))

# plot
ggraph(grafo)+
  geom_edge_link0(edge_colour = "grey66")+
  geom_node_point(aes(fill = ms$cluster),size=5,shape=21)

enter image description here

The above procedure does not consider the node weights, but I need to consider it and set some constraints.
The weights vector can be imported as follows:

# weights
w <- read.table('https://raw.githubusercontent.com/sergiocostafh/adjmatrix_example/main/weights.txt') %>% as.vector()

# adding the weights column to the dataset
ms$weight <- w

# calculating the total weight of each cluster
ms %>% group_by(cluster) %>% summarise(weight = sum(weight)) %>% arrange(-weight)

# A tibble: 12 x 2
   cluster weight
   <chr>    <dbl>
 1 2        429. 
 2 1        351. 
 3 6        330. 
 4 3        325. 
 5 5        194. 
 6 7        120. 
 7 4         80.9
 8 11        68.9
 9 10        57.4
10 8         53.6
11 9         42.0
12 12        32.9

By calculating the total weight of each cluster, we get 429 as the highest value (cluster 2) and 32.9 as the lowest (cluster 12), but I need to consider the following constraints:

  • Maximum cluster total weight: 400
  • Minimum cluster total weight: 50

I know the use of the cutat function that allows us to set the number of clusters, but this does not guarantee that the restrictions are met.

Perhaps there is a better package to solve this type of problem. Well I don't know.

Any help in solving this problem will be appreciated.