# How to cluster a network?

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Hello guys,
If I have a network ( Lets call it x) and it is described by the following edges:
x=[1 2 3 4 5 6]; %vertices in the network
Edg =[1 2; 1 3 ; 2 3 ; 3 4 ; 4 5;6 3; 5 6]; %edges
A=graph(Edg(:,1),Edg(:,2));
plot(A)
The graph A looks like this : If x is devided into two areas (we know the nodes in each area):
x1=[1 2 3];
x2=[3 4 5 6]; %the common vertex is 3
%edges is the same
Now i want to plot each area, so the graph above will be splitted into two graphs and vertix 3 is in both graphs.
To do this i need to write a code which gives the edges in each area, like this:
Edges for x1 [ 1 2; 2 3; 1 3]. Edges for x2 [ 3 6; 3 4; 4 5 ; 5 6].

Akira Agata on 14 Jul 2019
The following is an example:
% Sample Graph
s = [1 1 2 2 3 4 4 5 6 6 7 7 8];
t = [2 3 3 4 4 5 7 6 7 10 8 9 9];
G = graph(s,t);
% Visualize G
figure
plot(G);
% Apply biconncomp function
bincell = biconncomp(G, 'OutputForm', 'cell');
n = length(bincell);
% Visualize the separated graphs
figure
for ii = 1:n
subplot(2,2,ii)
plot(subgraph(G, bincell{ii}), 'NodeLabel', bincell{ii});
end
Original Graph: Separated graphs: #### 1 Comment

abdullah nasser abdullah on 17 Jul 2019
Your answer perfectly fit if there is only one coupled node between any two areas,
but lets consider that i have more than coupled node like the following:
x=[1 2 3 4 5 6]; %vertices in the network
Edg =[1 2; 1 4 ; 2 3 ; 3 4 ; 4 5;6 3; 5 6]; %edges
G=graph(Edg(:,1),Edg(:,2));
plot(G) And we want the paritioning to be like this: Where 3 and 4 are the common node between the two areas.
I want something that work for larger systems; where i know the nodes for each area and i know the coupled nodes between them as well.