Are there nice generalizations of SPQR trees to k-connected components for k>3? I'm curious how one should best understand the connections between the k-connected components when $G$ has minimum cuts of size $k&gt;3$, or perhaps approximate minimum cuts produced by Karger's algorithm.  SPQR trees answer this question for 2-connected graphs.  And obviously 1-connected graphs are simply a tree of their 2-connected components.
For edge connectivity rather than vertex connectivity, there's always the Gomory–Hu tree.