How do you find strongly connected components in a directed graph?

Kosaraju's algorithm: (1) DFS on original graph, pushing finished vertices to stack. (2) Transpose the graph. (3) Pop vertices from stack, DFS on transposed graph - each DFS tree is an SCC. O(V+E) time. Tarjan's algorithm uses single DFS with low-link values, identifying SCCs when a node's low-link equals its discovery time. Both find maximal sets where every vertex is reachable from every other vertex within the set.