finding all paths between two nodes in directed graph

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
//using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Collections.Specialized;
using System.Collections;

namespace Direct_Graph
{
  class Program
  {
    public class Digraph
    {
      private readonly int _v; //The number of vertices
      private int _e; //The number of edges
      private LinkedList<int>[] adj; //Use a LinkedList for the adjacency-list representation

      //Create a new directed graph with V vertices
      public Digraph(int V)
      {
        if (V < 0)
          throw new Exception("Number of vertices in a Digraph must be nonnegative");
          
        this._v = V;
        this._e = 0;
        //Create a new adjecency-list for each vertex
        adj = new LinkedList<int>[V];
        for (int v = 0; v < V; v++)
        {
          adj[v] = new LinkedList<int>();
        }
      }

      //return the number of vertices
      public int V()
      {
        return _v;
      }

      //return the number of edges
      public int E()
      {
        return _e;
      }

      //Add an edge to the directed graph from v to w
      public void AddEdge(int v, int w)
      {
        if (v < 0 || v >= _v) 
          throw new Exception("vertex " + v + " is not between 0 and " + (_v - 1));
        if (w < 0 || w >= _v)
          throw new Exception("vertex " + w + " is not between 0 and " + (_v - 1));
        
        adj[v].AddFirst(w);
        _e++;
      }

      /*
        * Return the adjacency-list for vertex v, which
        * are the vertices connected to v pointing from v
      * */
      public LinkedList<int> Adj(int v)
      {
        if (v < 0 || v >= _v) 
          throw new Exception();
      
        return adj[v];
      }

       //Return the directed graph as a string
       public String toString()
       {
         StringBuilder s = new StringBuilder();
         String NEWLINE = Environment.NewLine;
         //s.Append(_v + " vertices, " + _e + " edges " + NEWLINE);
         for (int v = 0; v < _v; v++)
         {
           s.Append(String.Format("{0:d}: ", v));
           foreach (int w in adj[v])
           {
             s.Append(String.Format("{0:d} ", w));
           }
           s.Append(NEWLINE);
         }
         return s.ToString();
       }
     }
  
    public class Search
    {
      int START;
      int END;

      public void DepthFirstSearch(Digraph graph, LinkedList<int> visited)
      {
        // int v = visited.Last();
                
        LinkedList<int> nodes = graph.Adj(visited.Last());
               
        // examine adjacent nodes
        foreach (int node in nodes)
        {
          if (visited.Contains(node))
            continue;

          if (node == END)
          {
            visited.AddFirst(node);
            printPath(visited);
            visited.RemoveLast();
            break;
          }
        }

        // in breadth-first, recursion needs to come after visiting adjacent nodes
        foreach (int node in nodes)
        {
          if (visited.Contains(node) || node == END)
            continue;
 
          visited.AddLast(node);
          DepthFirstSearch(graph, visited);
          visited.RemoveLast();
        }
      }

      public void printPath(LinkedList<int> visited)
      {
        foreach (int node in visited)
        {
          Console.Write(node);
          Console.Write(" ");
        }
        Console.WriteLine();
      }
    }

    static void Main(string[] args)
    {
      int START = 3;
      int END = 8;

      Digraph dg = new Digraph(30);

      dg.AddEdge(3, 4);
      dg.AddEdge(4, 8);
      dg.AddEdge(4, 11);
      dg.AddEdge(11, 14);
      dg.AddEdge(11, 17);
      dg.AddEdge(11, 8);
      dg.AddEdge(14, 8);
      dg.AddEdge(14, 17);
      dg.AddEdge(14, 25);
      dg.AddEdge(17, 22);
      dg.AddEdge(17, 25);
      dg.AddEdge(25, 8);
      dg.AddEdge(22, 25);
             
      LinkedList<int> visited = new LinkedList<int>();
      visited.AddFirst(START);
      Search s = new Search();
      s.DepthFirstSearch(dg, visited);
      s.printPath(visited);
    }
  }
}