create a community matrix, then find its laplacian matrix and then normalize the laplacian matrix in r

# Create a community matrix
community_matrix <- matrix(c(1,1,0,0,
                             1,1,0,0,
                             0,0,1,1,
                             0,0,1,1), nrow=4, byrow=TRUE)

# Find the Laplacian matrix
laplacian_matrix <- diag(rowSums(community_matrix)) - community_matrix

# Normalize the Laplacian matrix
D_half <- diag(sqrt(1/rowSums(community_matrix)))
normalized_laplacian <- D_half %*% laplacian_matrix %*% D_half

# Print the matrices
print("Community Matrix:")
print(community_matrix)
print("Laplacian Matrix:")
print(laplacian_matrix)
print("Normalized Laplacian Matrix:")
print(normalized_laplacian)
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