create a community matrix and use its laplacian matrix to get eigenvectors sorted by their corresponding eigenvalue in non-decreasing order. then use k means algorithm and plot a cluster graph in r

main.r
# Create a community matrix
community_matrix <- matrix(
  c(1, 1, 0, 0, 0, 
    1, 1, 0, 0, 0, 
    0, 0, 1, 1, 0, 
    0, 0, 1, 1, 1, 
    0, 0, 0, 1, 1),
  nrow = 5, byrow = TRUE
)

# Create Laplacian Matrix
laplacian_matrix <- diag(rowSums(community_matrix)) - community_matrix

# Compute eigenvectors and eigenvalues
laplacian_eigen <- eigen(laplacian_matrix)
sorted_eigenvectors <- laplacian_eigen$vectors[, order(laplacian_eigen$values)]

# K-means clustering
library(stats)
kmeans_result <- kmeans(sorted_eigenvectors[, 1:2], centers = 2)

# Plot cluster graph
library(ggplot2)
library(reshape2)

df <- data.frame(
  x = sorted_eigenvectors[, 1],
  y = sorted_eigenvectors[, 2],
  cluster = factor(kmeans_result$cluster)
)

ggplot(data = df, aes(x = x, y = y, color = cluster)) +
  geom_point() +
  labs(title = "Cluster Graph")
836 chars
35 lines