Graph Adjacency List Implementation

Question

I am trying to represent a Graph in Adjacency List using C#, like the code bellow. But I would like to know where I can find a better implementation in C#. Like this website for Java: http://algs4.cs.princeton.edu/41undirected/Graph.java.html

In order to improve this implementation I have some question:

1. Is there another simple data structure to use, and that you able to make operations like DFS,BFS, Find the Shortest-path easier ? Or the data structure vary too much according to the problem to be solved ?

=== EDITED ===

I've tried to implement the data structure as bellow.

OBS: This approach seems simple, but I realize later that is not very suitable for a DFS, for example, since you need to keep track of the first element of the LinkedList all the time.In my solution Seems that is better to use a custom created Linked List, instead of LinkedList<Vertex>.

Considering the comments bellow and to maintain simplicity I made some changes. But I don't know if that changes would affect further operations, like a BFS. To be able to have direct and indirect Graph I think is better to use an interface than a property.

 public interface IGraph
    {
        void InsertEdge(int edgeAKey, int edgeBKey);
        void IsertNewVertex(int vertexKey);
        LinkedList<Vertex> FindByKey(int vertexKey);
        bool ExistKey(int vertexKey);
    }

To make it as simple as possible we can use already implemented data structures like Dictionary and LinkedList. And instead of using an object as Dictionary key, to make it simple we can create in Vertex a key (or label) and a value, if you would like to add a value that already exist in another Vertex.

public class GraphDirect : IGraph
    {
        private Dictionary<int,LinkedList<Vertex>> Vertexes { get; set; }

        public GraphDirect()
        {
            Vertexes = new Dictionary<int, LinkedList<Vertex>>();
        }

        public bool ExistKey(int vertexKey)
        {
            if (this.FindByKey(vertexKey) == null)
                return false;
            else
                return true;
        }

        public void IsertNewVertex(int vertexKey)
        {
            if (!this.ExistKey(vertexKey))
            {
                Vertex vertex = new Vertex(vertexKey);
                LinkedList<Vertex> listVertexes = new LinkedList<Vertex>();
                listVertexes.AddFirst(vertex);
                this.Vertexes.Add(vertexKey, listVertexes);
            }
        }

        public void InsertEdge(int vertexAKey, int vertexBKey)
        {
            //Create the vertex A, if it doesn't exist            
            if (!this.ExistKey(vertexAKey))
            {
                this.IsertNewVertex(vertexAKey);
            } 
            //Will always insert the vertex B on this edge
            this.FindByKey(vertexAKey).AddLast(new Vertex(vertexBKey));
            //Create the vertex B, if doesn't exist
            if (!this.ExistKey(vertexBKey))
            {
                this.IsertNewVertex(vertexBKey);
            }
        }

        public LinkedList<Vertex> FindByKey(int vertexKey)
        {
            if (this.Vertexes.ContainsKey(vertexKey))
                return this.Vertexes[vertexKey];

            return null;
        }

    }

The Vertex class doesn't need any other pointer, just keep the key and a value, if necessary.

public enum State { Visited = 0, UnVisited = 1, Processed = 2 }

public class Vertex
{
    public int Key;
    public int Value;
    public State Status = State.UnVisited;

    public Vertex(int key)
    {
        this.Key = key;
        this.Value = 0;
    }

    public Vertex(int key, int value)
    {
        this.Key = key;
        this.Value = value;
    }
}

public class Start
{
     public static void Main(){
         GraphDirect gDirect = new GraphDirect();
         gDirect.InsertEdge(2, 3);
         gDirect.InsertEdge(2, 8);
         gDirect.InsertEdge(5, 6);
     }
}