Generalizations
The theory of clique-sums may also be generalized from graphs to matroids. Notably, Seymour's decomposition theorem characterizes the regular matroids (the matroids representable by totally unimodular matrices) as the 3-sums of graphic matroids (the matroids representing spanning trees in a graph), cographic matroids, and a certain 10-element matroid.
Read more about this topic: Clique-sum