def dense_dict_to_sparse_dict(fc_dict: dict) ->dict:
    """ Converts dense dict to sparse dict.

    This does not check if label symmetry is True, but rather will just keep
    the sorted clusters and their force constants.

    Parameters
    ----------
    fc_dict
        keys corresponding to clusters and values to the force constants
    """
    fc_dict_sparse = dict()
    for cluster, fc in fc_dict.items():
        if cluster == tuple(sorted(cluster)):
            fc_dict_sparse[cluster] = fc
    return fc_dict_sparse
