Kosaraju's Algorithm

One of the most common and conceptually easy to grasp methods of finding the strongly connected components of a graph is Kosaraju's algorithm. Kosaraju's algorithm works by performing two independent sets of DFS traversals, first exploring the graph in its original form, and then doing the same with its transpose.

Note

Though DFS is the type of traversal typically used in Kosaraju's algorithm, BFS is also a viable option. For the explanations and exercises included in this chapter, however, we will stick with the traditional DFS-based approach.

The transpose of a graph is essentially identical to the original graph, except that the source/destination vertices in each of its edges are swapped (that is, if there is an edge from node A to node B in the original graph, the transposed graph will have an edge from node B to node A):

Figure 7.16: Transpose of a graph

The first step of the algorithm (after initialization) is to iterate through the...