The biconncomp function will split the edges of a graph into its biconnected components. If the output of biconncomp is a vector of all ones, that graph is two-connected.
Otherwise, here's some code that will extract each biconnected component as an individual graph as follows:
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);
p = plot(G);
bins = biconncomp(G);
for binNr = 1:max(bins)
st = G.Edges.EndNodes;
Gbin = subgraph(G, unique(st(bins == binNr, :)));
figure;
plot(Gbin)
end
Keep in mind: For a graph without node names in MATLAB, nodes are numbered through 1, 2, ..., [number of nodes]. This means that the subgraph command can assign a new node index (e.g., if G has three nodes, subgraph(G, [1 3]) will return a graph where the previous node 3 is now node 2). You can avoid this by using node names.
