# Strongly Connected Component [Strong connected component | Wikipedia](https://en.wikipedia.org/wiki/Strongly_connected_component) > [!summary] Definition A _strongly connected component_ of a directed graph > $G = (V, E)$ is a maximal set of vertices $C \subseteq V$ such that for every > pair of vertices $u, v \in C$, both $u \leadsto v$ and $v \leadsto u$, i.e. > reachable from each other. - _Component graph_: $G^\text{SCC} = (V^\text{SCC}, E^\text{SCC})$, with the "contraction" technique. - Component graph is acyclic! - Procedures for computing - Call [[dfs|DFS]] on $G$ to compute finish times $u.f$ for each vertex - Create $G^\mathrm T$ - Call DFS of $G^\mathrm T$, but in the main loop consider vertices in order of decreasing $u.f$ - Output vertices of each tree