$\%---$ Parameters

a $=10$; $\%$ Mesh width

p $=0\mathrm{.}25$; $\%$ Link probability

$\%---$ Hexagonal mesh

$[$X$,$ Y$]=$ meshgrid$(1$:a$,1$:a$)$;

for i $=2$:$2$:a

X$($i$,$ :) $=$ X$($i$,$ :) $+0\mathrm{.}5$; $\%$ Correcting the offset for even rows

end

Y $=$ Y $*$ sqrt$(3)/2$;

x $=$ X$($:$)$;

y $=$ Y$($:$)$;

$\%---$ Random network generation

$\%$ Get delaunay triangulation

T $=$ delaunay$($x$,$ y$)$;

$\%$ Get a list of all links

tmp $=[$T$($:$,1)$ T$($:$,2)$; T$($:$,1)$ T$($:$,3)$; T$($:$,2)$ T$($:$,3)]$;

$\%$ Filter out duplicates

links $=$ unique$([$min$($tmp$($:$,1),$ tmp$($:$,2)),$ max$($tmp$($:$,1),$ tmp$($:$,2))],$ 'rows'$)$;

$\%$ Filter with probability p to get the random network

L $=$ links$($rand$($size$($links p$,$ :$)$;

$\%$ Get sparse adjacency matrix

A $=$ sparse$($L$($:$,1),$ L$($:$,2),$ ones$($size$($L$,1),1),$ a$^2,$ a$^2)$;

$\%$ Find clusters using the custom rcm method

tic;

C $=$ cluster$\_$custom$\_$rcm$($A$)$;

toc;

$\%$ Display clusters

figure;

hold on;

colors $=$ lines$($numel$($C$))$; $\%$ Generate distinct colors for each cluster

for i $=1$:numel$($C$)$

scatter$($x$($C$\{$i$\}),$ y$($C$\{$i$\}),100,$ 'filled', 'MarkerFaceColor', colors$($i$,$:$))$;

end

title$(\text{'}$Clusters found using custom K$-$means method'$)$;

xlabel$(\text{'}$X$\text{'})$;

ylabel$(\text{'}$Y$\text{'})$;

axis equal;

grid on; $\%$ Optional: add grid for better visualization

this is the matlab script

this is the matlab function:

function C $=$ cluster$\_$custom$\_$rcm$($A$)$

$\%$ Symmetrize adjacency matrix

S $=$ A $+$ A$\text{'}$;

$\%$ Reverse Cuthill$-$McKee ordering using your custom method

r $=$ ReverseCuthillMckee$($S$)$;

$\%$ Get the clusters

C $=\{$r$(1)\}$;

for i $=2$:numel$($r$)$

if any$($S$($C$\{$end$\},$ r$($i$)))$

C$\{$end$\}($end$+1)=$ r$($i$)$;

else

C$\{$end$+1\}=$ r$($i$)$;

end

end

like this create a custom kmeans function that creates clusters using kmeans clustering algorithm instead of reverse cuthill mckee algorithm

the output should look like the image attached $($but instead of reverse cuthill mckee algorithm for clustering use K$-$means $)$