For each follower, let Z be the total number of brands they follow.
    Return a dictionary of 1. / log(Z), for each follower.

def compute_log_degrees(brands, exemplars):
    """ For each follower, let Z be the total number of brands they follow.
    Return a dictionary of 1. / log(Z), for each follower.
    """
    counts = Counter()
    for followers in brands.values():  # + exemplars.values():  # Include exemplars in these counts? No, don't want to penalize people who follow many exemplars.
        counts.update(followers)
    counts.update(counts.keys())  # Add 1 to each count.
    for k in counts:
        counts[k] = 1. / math.log(counts[k])
    return counts