В рамках данной задачи предлагаю использовать Newtonsoft.
Установить пакет можно через NuGet в вижле.

class Program
    {
        const string pathData = @"c:\data.dat";
        static void Main(string[] args)
        {
            WriteData(GenerateData());
            DisplayListData(ReadData());
            Console.ReadLine();
        }

        static List<Cell> GenerateData()
        {
            List<Cell> dataCell = new List<Cell>();
            for (int i = 1; i <= 5; i++)
            {
                int val = i * 10;
                Cell cell = new Cell()
                {
                    neighbors = new List<int>() {val, val + 1, val + 2},
                    index = i
                };
                dataCell.Add(cell);
            }
            return dataCell;
        }

        static void WriteData(List<Cell> dataCell)
        {
            using (StreamWriter file = File.CreateText(pathData))
            {
                JsonSerializer serializer = new JsonSerializer();
                serializer.Serialize(file, dataCell);
            }
            Console.WriteLine("Save Data in PATH: " + pathData);
        }

        static List<Cell> ReadData()
        {
            using (StreamReader file = File.OpenText(pathData))
            {
                JsonSerializer serializer = new JsonSerializer();
                return (List<Cell>) serializer.Deserialize(file, typeof(List<Cell>));
            }
        }

        static void DisplayListData(List<Cell> dataList)
        {
            Console.WriteLine(new String('-', 5));
            foreach (var cell in dataList)
            {
                Console.WriteLine("Cell index: " + cell.index);
                Console.WriteLine(new String('-', 5));
                for (int i = 0; i < cell.neighbors.Count; i++)
                {
                    Console.WriteLine("Value index: " + i + " = " + cell.neighbors[i].ToString());
                }
                Console.WriteLine(new String('-', 5));
            }
        }
    }

    [Serializable]
    public class Cell
    {
        public List<int> neighbors { get; set; }
        public int index { get; set; }
    }

Думаю общий принцип понятен.