title: What are the articulation points of this directed graph?
body: <p>5 nodes in this directed graph.</p>
  
  <p>Edges:</p>
  
  <p>1 -> 2</p>
  
  <p>2 -> 3</p>
  
  <p>2 -> 4</p>
  
  <p>4 -> 5</p>
  
  <p>(Graphical image : <a href="http://i.imgur.com/hafBv.jpg" rel="nofollow">http://i.imgur.com/hafBv.jpg</a> )</p>
  
  <p>Am I correct in thinking that the articulation points are node 2 and 4 ?
  (If you remove node 2 or node 4, the graph becomes disconnected)</p>
  
  <p>But the definition I've seen everywhere says something similar to:</p>
  
  <blockquote>
    <p>a node u is an articulation point, if for every child v of u, there is no back edge from v to a node higher in the DFS tree than u. </p>
  </blockquote>
  
  <p>How does this work for a directed graph? For example, Node 3 does not have a back edge to a node higher in the DFS tree than 2. Does this classify Node 3 as an articulation point? But its removal does not cause the graph to be broken into 2 or more pieces (That is my layman definition of an articulation node).</p>