Getting minimum spanning tree using Prim algorithm on C#

Graph.cs

using System.Collections.Generic;

namespace PrimAlgorithm {
  public class Graph<T> {
    private List<Node> nodes_ = new List<Node>();

    public class Node {
      private List<Edge> edges_ = new List<Edge>();
      private T context_;

      public T context {
        get {
          return context_;
        }
      }

      public List<Edge> edges {
        get {
          return edges_;
        }
      }

      public Node (T context) {
        context_ = context;
      }
    }

    public class Edge {
      Node to_;
      int weight_;

      public Node to {
        get {
          return to_;
        }
      }
      public int weight {
        get {
          return weight_;
        }
      }

      public Edge (Node to, int weight) {
        to_ = to;
        weight_ = weight;
      }
    }

    public int n {
      get {
        return nodes_.Count;
      }
    }

    public List<Node> nodes {
      get {
        return nodes_;
      }
    }

    public Graph (IEnumerable<T> initialize_list) {
      foreach (var i in initialize_list) {
        AddVertex(i);
      }
    }

    public Graph (Graph<T> othr) {
      CopyFrom(othr);
    }

    public Node AddVertex (T context) {
      Node a = new Node(context);
      nodes_.Add(a);
      return a;
    }

    public Node FindVertex (T context) {
      return nodes_.Find(n => n.context.Equals(context));
    }

    public void CopyFrom (Graph<T> othr) {
      nodes_.Clear();
      nodes_.AddRange(othr.nodes_);
    }

    public bool Contains (Node node) {
      return nodes_.Find(n => n.Equals(node)) != null;
    }

    public void Remove (Node node) {
      nodes_.Remove(node);
    }
  }
}

GraphController.cs

using System.Collections.Generic;

namespace PrimAlgorithm.GraphController {
  public static class Controller {
    public static void SetEdge<T> (this Graph<T> self, T a, T b, int weight) {
      var a_node = self.FindVertex(a);
      var b_node = self.FindVertex(b);
      a_node.AddEdge(b_node, weight);
      b_node.AddEdge(a_node, weight);
    }

    public static void AddEdge<T> (this Graph<T>.Node self, Graph<T>.Node to, int weight) {
      self.edges.Add(new Graph<T>.Edge(to, weight));
    }

    public static List<Graph<T>.Node> GetNeighbors<T> (this Graph<T>.Node self) {
      return self.edges.ConvertAll(e => e.to);
    }

    public static int GetWeight<T> (this Graph<T>.Node self, Graph<T>.Node b) {
      foreach (var e in self.edges) {
        if (e.to == b) {
          return e.weight;
        }
      }
      return int.MaxValue - 1;
    }
  }
}

Prim.cs

using PrimAlgorithm.GraphController;
using System.Collections.Generic;

namespace PrimAlgorithm {
  class Prim<T> {
    readonly int kInfinite = int.MaxValue - 1;

    public void prim (Graph<T> g, Graph<T>.Node r, ref Dictionary<Graph<T>.Node, Graph<T>.Node> tree) {
      Graph<T> Q = new Graph<T>(g);
      var d = new Dictionary<Graph<T>.Node, int>();
      foreach (var u in Q.nodes) {
        d[u] = kInfinite;
      }
      d[r] = 0;

      while (Q.n > 0) {
        var u = deleteMin(Q, d);
        foreach (var v in u.GetNeighbors()) {
          if (Q.Contains(v) && (u.GetWeight(v) < d[v])) {
            d[v] = u.GetWeight(v);
            tree[v] = u;
          }
        }
      }
    }

    private Graph<T>.Node deleteMin (Graph<T> Q, Dictionary<Graph<T>.Node, int> d) {
      Graph<T>.Node min_node = null;
      int min_weight = kInfinite;
      foreach (var n in Q.nodes) {
        if (d[n] <= min_weight) {
          min_weight = d[n];
          min_node = n;
        }
      }
      Q.Remove(min_node);
      return min_node;
    }

  }
}

Program.cs

using PrimAlgorithm.GraphController;
using System;
using System.Collections.Generic;
using System.Linq;

namespace PrimAlgorithm {
  class Program {
    static void Main (string[] args) {
      Graph<int> W = new Graph<int>(Enumerable.Range(0, 8));
      
      W.SetEdge(0, 1, 8);
      W.SetEdge(0, 2, 9);
      W.SetEdge(0, 3, 11);

      W.SetEdge(1, 4, 10);

      W.SetEdge(2, 3, 13);
      W.SetEdge(2, 4, 5);
      W.SetEdge(2, 5, 12);

      W.SetEdge(3, 6, 8);
      W.SetEdge(5, 6, 7);

      Prim<int> prim = new Prim<int>();
      Dictionary<Graph<int>.Node, Graph<int>.Node> tree = new Dictionary<Graph<int>.Node, Graph<int>.Node>();
      prim.prim(W, W.FindVertex(0), ref tree);

      foreach(var kv in tree) {
        Console.WriteLine("{0} => {1}", kv.Key.context, kv.Value.context);
      }
    }
  }
}

Excuseme, my name Ilyas Hanif and i'am from Indonesia, and i'am very interested with your discussing, but i can't understand with your function code, i hope you can give an explanation or commented on your code, and i hope you can help me, thank you

Hi Ilyas Hanif,
Sure, I'll do comments soon.
Thanks

@ilyashanif sorry, it's late.
I think it would be better that you look an article written well than my explanation.
I recommend you these article and video.
https://www.geeksforgeeks.org/prims-minimum-spanning-tree-mst-greedy-algo-5/
https://www.youtube.com/watch?v=z1L3rMzG1_A
Thanks.

you should probably have the prim's method return the minimum cost which I had to manually do but other than that, thanks for providing a good example that uses an adjacency list, unlike the other examples that I could find.