How to detect if a directed graph is cyclic?

Question

How can we detect if a directed graph is cyclic? I thought using breadth first search, but I\'m not sure. Any ideas?

Answer 1

Use DFS to search if any path is cyclic

class Node { T value; List> adjacent;  }

class Graph{

    List> nodes;

   public boolean isCyclicRec()
   {

      for (Node node : nodes)
      {
            Set> initPath = new HashSet<>();
            if (isCyclicRec(node, initPath))
            {
              return true;
            }
      }
      return false;
   }

   private boolean isCyclicRec(Node currNode, Set> path)
   {
      if (path.contains(currNode))
      {
        return true;
      }
      else
      {
        path.add(currNode);
        for (Node node : currNode.adjacent)
        {
            if (isCyclicRec(node, path))
            {
                return true;
            }
            else
            {
                path.remove(node);
            }
        }
      }
      return false;
  }