MATLAB: Select edges that connect subgraphs together

graph theoryselect edges that connect subgraphs together

I have a graph like this
M = [1 2; 2 3; 1 3; 4 5; 5 6; 6 7; 4 7;2 4; 5 7; 5 8;11 8; 8 9; 9 10; 10 11;4 12; 12,13; 13 14;12 14];
g = graph(M(:, 1), M(:, 2));
h = plot(g);
I want to find edges that connect subgraphs together
result should be
A = [2,4; 5 8; 4 12]

Best Answer

This works for your sample data set (which does not include nodes 12:14 as shown in the plot. Please test test this, I'm not a graph theory expert so there may be cases where this does not work.
M = [1 2; 2 3; 1 3; 4 5; 5 6; 6 7; 4 7;2 4; 5 7; 5 8;11 8; 8 9; 9 10; 10 11];
g = graph(M(:, 1), M(:, 2));
h = plot(g);
bcg = biconncomp(g).'; % biconnected components
[count, group] = groupcounts(bcg); % How many of each?
edgeidx = ismember(bcg, group(count==1)); % Edges with one count
g.Edges(edgeidx, 1) % Extract
ans =
  2×1 table
    EndNodes
    ________
     2    4 
     5    8
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