title: Detecting a cycle in a directed graph
body: <p>I read a discussion <a href="https://stackoverflow.com/a/19115118/3880275">here</a>, at SO about finding a cycle in a directed graph. Now, the OP claims that we need to validate <strong>two</strong> things: </p>
  
  <ol>
  <li>There's a back edge from <code>u</code> to <code>v</code></li>
  <li><code>v</code> is in the recursion-stack</li>
  </ol>
  
  <p>Why do we need the second test? Could you give an example to demonstrate it's necessity? </p>