def average_coordination_number(structures, freq=10):
    """
    Calculates the ensemble averaged Voronoi coordination numbers
    of a list of Structures using VoronoiNN.
    Typically used for analyzing the output of a Molecular Dynamics run.
    Args:
        structures (list): list of Structures.
        freq (int): sampling frequency of coordination number [every freq steps].
    Returns:
        Dictionary of elements as keys and average coordination numbers as values.
    """
    coordination_numbers = {}
    for spec in structures[0].composition.as_dict().keys():
        coordination_numbers[spec] = 0.0
    count = 0
    for t in range(len(structures)):
        if t % freq != 0:
            continue
        count += 1
        vnn = VoronoiNN()
        for atom in range(len(structures[0])):
            cn = vnn.get_cn(structures[t], atom, use_weights=True)
            coordination_numbers[structures[t][atom].species_string] += cn
    elements = structures[0].composition.as_dict()
    for el in coordination_numbers:
        coordination_numbers[el] = coordination_numbers[el] / elements[
            el] / count
    return coordination_numbers
Calculates the ensemble averaged Voronoi coordination numbers
    of a list of Structures using VoronoiNN.
    Typically used for analyzing the output of a Molecular Dynamics run.
    Args:
        structures (list): list of Structures.
        freq (int): sampling frequency of coordination number [every freq steps].
    Returns:
        Dictionary of elements as keys and average coordination numbers as values.