Tarjan's Algorithm - Steps

Tarjan's algorithm maintains a stack of nodes in the current DFS path and tracks two arrays: disc[v]: Discovery time when node $v$ was first visited. low[v]: Minimum of disc[v], low[u] for all children $u$, and disc[w] for all back edges $v \to w$ where $w$ is on the stack.

When you finish processing node $v$, check if low[v] = disc[v]. If yes, $v$ is the root of an SCC. Pop all nodes from stack down to and including $v$. Assign them all the same component ID.