Building Biconnected Components

$1.$ Find all articulation points using Tarjan's algorithm.

$2.$ Use a stack to track edges during DFS.

When you backtrack from a child $v$ where low[v] >= disc[u], pop edges from the stack until you reach $(u, v)$. These edges form a biconnected component.

$3.$ Each biconnected component is defined by the edges (and their incident vertices) popped in step $2$. This is more complex than $2$-edge-connected components because you need to track edge stacks during DFS.