Bidirectional 1 to 1 Dictionary in C#

OK, here is my attempt (building on Jon’s – thanks), archived here and open for improvement :

/// <summary>
/// This is a dictionary guaranteed to have only one of each value and key. 
/// It may be searched either by TFirst or by TSecond, giving a unique answer because it is 1 to 1.
/// </summary>
/// <typeparam name="TFirst">The type of the "key"</typeparam>
/// <typeparam name="TSecond">The type of the "value"</typeparam>
public class BiDictionaryOneToOne<TFirst, TSecond>
{
    IDictionary<TFirst, TSecond> firstToSecond = new Dictionary<TFirst, TSecond>();
    IDictionary<TSecond, TFirst> secondToFirst = new Dictionary<TSecond, TFirst>();

    #region Exception throwing methods

    /// <summary>
    /// Tries to add the pair to the dictionary.
    /// Throws an exception if either element is already in the dictionary
    /// </summary>
    /// <param name="first"></param>
    /// <param name="second"></param>
    public void Add(TFirst first, TSecond second)
    {
        if (firstToSecond.ContainsKey(first) || secondToFirst.ContainsKey(second))
            throw new ArgumentException("Duplicate first or second");

        firstToSecond.Add(first, second);
        secondToFirst.Add(second, first);
    }

    /// <summary>
    /// Find the TSecond corresponding to the TFirst first
    /// Throws an exception if first is not in the dictionary.
    /// </summary>
    /// <param name="first">the key to search for</param>
    /// <returns>the value corresponding to first</returns>
    public TSecond GetByFirst(TFirst first)
    {
        TSecond second;
        if (!firstToSecond.TryGetValue(first, out second))
            throw new ArgumentException("first");

        return second; 
    }

    /// <summary>
    /// Find the TFirst corresponing to the Second second.
    /// Throws an exception if second is not in the dictionary.
    /// </summary>
    /// <param name="second">the key to search for</param>
    /// <returns>the value corresponding to second</returns>
    public TFirst GetBySecond(TSecond second)
    {
        TFirst first;
        if (!secondToFirst.TryGetValue(second, out first))
            throw new ArgumentException("second");

        return first; 
    }


    /// <summary>
    /// Remove the record containing first.
    /// If first is not in the dictionary, throws an Exception.
    /// </summary>
    /// <param name="first">the key of the record to delete</param>
    public void RemoveByFirst(TFirst first)
    {
        TSecond second;
        if (!firstToSecond.TryGetValue(first, out second))
            throw new ArgumentException("first");

        firstToSecond.Remove(first);
        secondToFirst.Remove(second);
    }

    /// <summary>
    /// Remove the record containing second.
    /// If second is not in the dictionary, throws an Exception.
    /// </summary>
    /// <param name="second">the key of the record to delete</param>
    public void RemoveBySecond(TSecond second)
    {
        TFirst first;
        if (!secondToFirst.TryGetValue(second, out first))
            throw new ArgumentException("second");

        secondToFirst.Remove(second);
        firstToSecond.Remove(first);
    }

    #endregion

    #region Try methods

    /// <summary>
    /// Tries to add the pair to the dictionary.
    /// Returns false if either element is already in the dictionary        
    /// </summary>
    /// <param name="first"></param>
    /// <param name="second"></param>
    /// <returns>true if successfully added, false if either element are already in the dictionary</returns>
    public Boolean TryAdd(TFirst first, TSecond second)
    {
        if (firstToSecond.ContainsKey(first) || secondToFirst.ContainsKey(second))
            return false;

        firstToSecond.Add(first, second);
        secondToFirst.Add(second, first);
        return true;
    }


    /// <summary>
    /// Find the TSecond corresponding to the TFirst first.
    /// Returns false if first is not in the dictionary.
    /// </summary>
    /// <param name="first">the key to search for</param>
    /// <param name="second">the corresponding value</param>
    /// <returns>true if first is in the dictionary, false otherwise</returns>
    public Boolean TryGetByFirst(TFirst first, out TSecond second)
    {
        return firstToSecond.TryGetValue(first, out second);
    }

    /// <summary>
    /// Find the TFirst corresponding to the TSecond second.
    /// Returns false if second is not in the dictionary.
    /// </summary>
    /// <param name="second">the key to search for</param>
    /// <param name="first">the corresponding value</param>
    /// <returns>true if second is in the dictionary, false otherwise</returns>
    public Boolean TryGetBySecond(TSecond second, out TFirst first)
    {
        return secondToFirst.TryGetValue(second, out first);
    }

    /// <summary>
    /// Remove the record containing first, if there is one.
    /// </summary>
    /// <param name="first"></param>
    /// <returns> If first is not in the dictionary, returns false, otherwise true</returns>
    public Boolean TryRemoveByFirst(TFirst first)
    {
        TSecond second;
        if (!firstToSecond.TryGetValue(first, out second))
            return false;

        firstToSecond.Remove(first);
        secondToFirst.Remove(second);
        return true;
    }

    /// <summary>
    /// Remove the record containing second, if there is one.
    /// </summary>
    /// <param name="second"></param>
    /// <returns> If second is not in the dictionary, returns false, otherwise true</returns>
    public Boolean TryRemoveBySecond(TSecond second)
    {
        TFirst first;
        if (!secondToFirst.TryGetValue(second, out first))
            return false;

        secondToFirst.Remove(second);
        firstToSecond.Remove(first);
        return true;
    }

    #endregion        

    /// <summary>
    /// The number of pairs stored in the dictionary
    /// </summary>
    public Int32 Count
    {
        get { return firstToSecond.Count; }
    }

    /// <summary>
    /// Removes all items from the dictionary.
    /// </summary>
    public void Clear()
    {
        firstToSecond.Clear();
        secondToFirst.Clear();
    }
}