A tree data structure for C# Net Core

TreeNode.cs

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

namespace Trees1
{
    class Program
    {
        static void Main(string[] args)
        {
            var tree = new TreeNode("Root")
            {
                new TreeNode("Cat 1")
                {
                    new TreeNode("Item 1"),
                    new TreeNode("Item 2"),
                    new TreeNode("Item 3"),
                },
                new TreeNode("Cat 2")
                {
                    new TreeNode("Item 1"),
                    new TreeNode("Item 2"),
                    new TreeNode("Item 3"),
                }
            };
        }
    }

    public class TreeNode : IEnumerable<TreeNode>
    {
        private readonly Dictionary<string, TreeNode> children = new Dictionary<string, TreeNode>();

        public readonly string Id;
        public TreeNode Parent { get; set; }

        public TreeNode(string id)
        {
            this.Id = id;
        }

        public TreeNode GetChild(string id)
        {
            return this.children[id];
        }

        public void Add(TreeNode item)
        {
            if (item.Parent != null)
            {
                item.Parent.children.Remove(item.Id);
            }

            item.Parent = this;
            this.children.Add(item.Id, item);
        }

        public IEnumerator<TreeNode> GetEnumerator()
        {
            return this.children.Values.GetEnumerator();
        }

        IEnumerator IEnumerable.GetEnumerator()
        {
            return (IEnumerator)GetEnumerator();
        }

        public int Count
        {
            get {  return this.children.Count;}
        }
    }
}