can you create the code fr R that runs the louvain algorithm on a network of $20$ nodes and is undirected where it visualises$/$plots each step$($ modularity optimization and community aggregation$).$ I have used the following code and works apart from it doesnt have edges between the nodes in the community aggregation graph: # Load necessary library

library$($igraph$)$

# Define the edges of your network $($adjust as needed$)$

edges $<-$ c$($

$1,2,1,3,1,4,1,5,$

$2,3,2,4,2,5,2,6,$

$3,4,3,5,3,6,3,7,$

$4,5,4,6,4,7,4,8,$

$5,6,5,7,5,8,5,9,$

$6,7,6,8,6,9,6,10,$

$7,8,7,9,7,10,7,11,$

$8,9,8,10,8,11,8,12,$

$9,10,9,11,9,12,9,13,$

$10,11,10,12,10,13,10,14,$

$11,12,11,13,11,14,11,15,$

$12,13,12,14,12,15,12,16,$

$13,14,13,15,13,16,13,17,$

$14,15,14,16,14,17,14,18,$

$15,16,15,17,15,18,15,19,$

$16,17,16,18,16,19,16,20,$

$17,18,17,19,17,20,$

$18,19,18,20,$

$19,20$

$)$

# Create the initial graph $($ensure it's undirected$)$

graph $<-$ graph$($edges$,$ directed $=$ FALSE$)$

# Initial plot

plot$($graph$,$ main $=$ "Original Network"$)$

# Step $1$: Modularity Optimization

louvain$\_$partition $<-$ cluster$\_$louvain$($graph$)$

# Visualize the modularity optimization

plot$($louvain$\_$partition, graph, main $=$ "Modularity Optimization"$)$

# Step $2$: Community Aggregation

while $($TRUE$)\{$

previous$\_$partition $<-$ louvain$\_$partition

# Create a new graph with each unique community as a single node

unique$\_$communities $<-$ unique$($membership$($louvain$\_$partition$))$

aggregated$\_$graph $<-$ make$\_$empty$\_$graph$($n $=$ length$($unique$\_$communities$),$ directed $=$ FALSE$)$

V$($aggregated$\_$graph$)$$name $<-$ as$.$character$($unique$\_$communities$)$

# Iterate through original edges and add edges between communities

for $($i in $1$:$($length$($edges$)/2))\{$

from$\_$node $<-$ edges$[2*$ i $-1]$

to$\_$node $<-$ edges$[2*$ i$]$

from$\_$comm $<-$ membership$($louvain$\_$partition$)[$from$\_$node$]$

to$\_$comm $<-$ membership$($louvain$\_$partition$)[$to$\_$node$]$

if $(!$is$.$na$($from$\_$comm$)$ && $!$is$.$na$($to$\_$comm$)$ && from$\_$comm $!=$ to$\_$comm$)\{$

from$\_$vertex $<-$ which$($V$($aggregated$\_$graph$)$$name $==$ as$.$character$($from$\_$comm$))$

to$\_$vertex $<-$ which$($V$($aggregated$\_$graph$)$$name $==$ as$.$character$($to$\_$comm$))$

add$\_$edges$($aggregated$\_$graph, c$($from$\_$vertex, to$\_$vertex$))$

$\}$

$\}$

# Re$-$run modularity optimization on aggregated graph

louvain$\_$partition $<-$ cluster$\_$louvain$($aggregated$\_$graph$)$

# Visualize the community aggregation

plot$($louvain$\_$partition, aggregated$\_$graph, main $=$ "Community Aggregation"$)$

# Check for convergence

if $($identical$($membership$($previous$\_$partition$),$ membership$($louvain$\_$partition$)))\{$

break

$\}$

$\}$