C# Challenge:

Main Method:

using System;
namespace DailyProgrammer_NodeGraph
{
    /* https://www.reddit.com/r/dailyprogrammer/comments/4ijtrt/20160509_challenge_266_easy_basic_graph/ */
    public class Program
    {
        static void Main(string[] args)
        {
            var test = new NodeGraph();
            Console.WriteLine("Press enter to exit..." + Console.ReadLine());
        }
    }
}

node graph class:

using System.Collections.Generic;
using System.IO;

namespace DailyProgrammer_NodeGraph
{
    public class NodeGraph
    {
        private List<Node> Graph = new List<Node>();
        public NodeGraph()
        {
            GetInput();
            PrintAll();
        }
        public void AddEdgeToGraph(int edgeID, int nodeID)
        {
            var edge = Graph.Find(e => e.Equals(edgeID));
            if (edge != null)
            {
                Graph.Find(q => q.Equals(nodeID)).AddEdge(edge);
            }
        }
        private void GetInput()
        {
            var directory = Directory.GetCurrentDirectory();
            var r = new StreamReader(directory + @"\input.txt");
            var max = int.Parse(r.ReadLine());
            InitNodes(max);

            var split = r.ReadLine();
            while (split != null)
            {
                var text = split.Split(' ');
                var id1 = int.Parse(text[0]);
                var id2 = int.Parse(text[1]);
                AddEdgeToGraph(id2, id1);
                split = r.ReadLine();
            }
        }
        private void InitNodes(int numNodes)
        {
            for (var i = 1; i <= numNodes; i++)
            {
                var n = new Node(i);
                Graph.Add(n);
            }
        }
        private void PrintAll()
        {
            foreach (var n in Graph)
            {
                n.PrintAll();
            }
        }
    }
}

Node Class:

using System;
using System.Collections.Generic;
namespace DailyProgrammer_NodeGraph
{
    public class Node
    {
        private List<Node> _edges = new List<Node>();
        public int degree { get; set; }
        private int NodeId { get; set; }

        public Node(int nodeId)
        {
            NodeId = nodeId;
        }

        public int GetCountOfEdges()
        {
            return _edges.Count;
        }

        public bool Equals(int id)
        {
            return NodeId == id;
        }

        public void AddEdge(Node n)
        {
            n.degree += 1;
            degree += 1;
            _edges.Add(n);
        }
        public void PrintAll()
        {
            Console.WriteLine("Node: {0} has a degree of {1}.", NodeId, degree);
        }
    }
}

Output:

Node: 1 has a degree of 8.
Node: 2 has a degree of 8.
Node: 3 has a degree of 6.
Node: 4 has a degree of 3.
Node: 5 has a degree of 7.
Node: 6 has a degree of 10.
Node: 7 has a degree of 7.
Node: 8 has a degree of 7.
Node: 9 has a degree of 7.
Node: 10 has a degree of 5.
Node: 11 has a degree of 9.
Node: 12 has a degree of 8.
Node: 13 has a degree of 8.
Node: 14 has a degree of 5.
Node: 15 has a degree of 9.
Node: 16 has a degree of 9.
Press enter to exit...