Strongly connected components

Input

A directed graph [math]\displaystyle{ G=(V,A) }[/math].

Output

A set of sets of nodes. Each set of nodes contains exactly the nodes of one SCC. The correspndence between the SCC and these sets of nodes is one-to-one.

Pseudocode

STRONGLY-CONNECTED-COMPONENTS(D)

STRONGLY-CONNECTED-COMPONENTS(D)
1 call DFS(D) to compute finishing times f[v] for each vertex v ∈ V
2 compute DT (w.r.t. step 3)
3 call DFS(DT), but in the main loop of DFS, consider the vertices in order of decreasing f[v] as computed in step 1
4 output the vertices of each tree in the DFS forest of step 3 as a separate strongly connected component

Known algorithms

1. Kosaraju

Further information

STRONGLY-CONNECTED-COMPONENTS runs in linear time.