How to cluster a network?

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].

Answer 1

[Akira Agata]

How about applying biconncomp function?

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:

[abdullah nasser abdullah]

Many thanks for your answer Mr. Akira,

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.