title: What if I do not use G transpose in calculating Strongly Connected Components?
body: <p>I am reading Introduction to Algorithms. In 22.5 Strongly Connected Component, the algorithm STRONGLY-CONNECTED-COMPONENT(G) is defined as:</p>
  
  <ol>
  <li>Call DFS(G) to compute finishing times u.f for each vertex u</li>
  <li>Compute G transpose</li>
  <li>Call DFS(G transpose), but in the main loop of DFS, consider the vertices in order of decreasing u.f(as computed in line 1)</li>
  <li>Output the vertices of each tree in the depth-first forest formed in line 3 as a separate strongly connected component</li>
  </ol>
  
  <p>If I change the alogrithm to just using G, without calculating G transpose. Also consider the vertices in order of Increasing u.f(Reverse order of topological sort):</p>
  
  <ol>
  <li>Call DFS(G) to compute finishing times u.f for each vertex u</li>
  <li>Call DFS(G), but in the main loop of DFS, consider the vertices in order of increasing u.f(as computed in line 1)</li>
  <li>Output the vertices of each tree in the depth-first forest formed in line 2</li>
  </ol>
  
  <p>Why is this algorithm wrong?</p>