Removing node from graph structure c#

Question

I'm self-learning c# and I'm a little confused on nodes in graph structures. I've cobbled together this code so far, but I have no idea how to remove and entire node from the list:

public class Graph
{
    private int _V;
    private int _E;
    private LinkedList<Int32>[] adj;

    public Graph(int V)
    {
        this._V = V;
        adj = new LinkedList<Int32>[_V];
        for (int v = 0; v < _V; v++)
        {
            adj[v] = new LinkedList<Int32>();
        }
    }

    public void AddEdge(int v, int w)
    {
        _E++;
        adj[v].AddFirst(w);
        adj[w].AddFirst(v);
    }

    public void RemoveEdge(int v, int w)
    {
        _E--;
        adj[v].Remove(w);
        adj[w].Remove(v);
    }

    public IEnumerable<Int32> Adj(int v)
    {
        return adj[v];
    }

    public int V()
    {
        return _V;
    }

    public bool isLeaf(int v)
    {
        return adj[v].Count() == 1;
    }

    public int adjacencies(int v)
    {
        return adj[v].Count();
    }

    public String toString()
    {
        StringBuilder s = new StringBuilder();
        String NEWLINE = Environment.NewLine;
        s.Append(adj[1].Count + 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();
    }

}

So, if I have four nodes where node 1 has an edge to 2, 2 has edges to both 3 and 4, and 3 and 4 share an edge with each other, I want to remove node 1 completely since it's a leaf. I can remove the edge easily enough, but that node still remains in my list (just without an edge). How do I get rid of 1 completely? I thought I should be able to just do a adj.Remove(1), but that throws an error.

I realize this is probably super easy, but the answers I've looked through in here seem to be describing something different or I'm simply not getting how this works.

Thanks!

Answer 1

Arrays do not support removal. If you really need to encode the concept of "does not exist" into adj , then you could set adj[v] to a value that represents "does not exist". For example,

adj[v] = null.

Alternatively, you could store adjacencies in a Dictionary<Int32> . Instead of

private LinkedList<Int32>[] adj;

you would have

private Dictionary<Int32, LinkedList<Int32>> adj;

and you could remove vertex v by

adj.Remove(v); // don't forget to remove the edges

In either case, you would probably want to update the other methods to handle such "removed" vertices.