Tarjan's Algorithm - Intuition

Tarjan's algorithm finds all SCCs in a single DFS pass using discovery times and low-link values. For each node $v$, track two values: disc[v] (when $v$ was first discovered) and low[v] (the lowest discovery time reachable from $v$'s subtree, including back edges).

When low[v] = disc[v], node $v$ is the root of an SCC. At this point, pop all nodes from the stack until you reach $v$. All popped nodes (including $v$) form one complete SCC.