def count_common_connections(network, user_A, user_B):
    """
    Finds the number of people that user_A and user_B have in common.
    Arguments:
    network: the gamer network data structure.
    user_A:  a string containing the name of user_A.
    user_B:  a string containing the name of user_B.
    Returns:
    The number of connections in common (as an integer).
    - If user_A or user_B is not in network, returns False.
    """
    count = 0
    if user_A not in network or user_B not in network:
        return False
    for person in network[user_A][0]:
        if person in network[user_B][0]:
            count += 1
    return count