write a code that takes a community matrix and does spectral analysis using laplacian matrix and plots a cluster graph in r

main.r
library(igraph)

# 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, 0,
                              0, 0, 0, 0, 1), nrow = 5, byrow = TRUE)

# Create an adjacency matrix from the community matrix
adjacency_matrix <- community_matrix %*% t(community_matrix)

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

# Get Laplacian matrix
laplacian_matrix <- laplacian_matrix(graph)

# Spectral analysis
eigen_values <- eigen(laplacian_matrix)$values

# Create a graph plot
plot(graph,vertex.color=V(graph)$community, main="Cluster Graph")

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