In the Twitter blogosphere, the number of followers is probably the most basic and succinct quantity for measuring popularity of users. However, the number of followers can be manipulated in various ways; we can even buy follows. Therefore, alternative popularity measures for Twitter users on the basis of, for example, users' tweets and retweets, have been developed. In the present work, we take a purely network approach to this fundamental question. First, we find that two relatively distinct types of users possessing a large number of followers exist, in particular for Japanese, Russian, and Korean users among the seven language groups that we examined. A first type of user follows a small number of other users. A second type of user follows approximately the same number of other users as the number of follows that the user receives. Then, we compare local (i.e., egocentric) followership networks around the two types of users with many followers. We show that the second type, which is presumably uninfluential users despite its large number of followers, is characterized by high link reciprocity, a large number of friends (i.e., those whom a user follows) for the followers, followers' high link reciprocity, large clustering coefficient, large fraction of the second type of users among the followers, and a small PageRank. Our network-based results support that the number of followers used alone is a misleading measure of user's popularity. We propose that the number of friends, which is simple to measure, also helps us to assess the popularity of Twitter users.