  Social media, regarded as two-layer networks consisting of users and items,
turn out to be the most important channels for access to massive information in
the era of Web 2.0. The dynamics of human activity and item popularity is a
crucial issue in social media networks. In this paper, by analyzing the growth
of user activity and item popularity in four empirical social media networks,
i.e., Amazon, Flickr, Delicious and Wikipedia, it is found that cross links
between users and items are more likely to be created by active users and to be
acquired by popular items, where user activity and item popularity are measured
by the number of cross links associated with users and items. This indicates
that users generally trace popular items, overall. However, it is found that
the inactive users more severely trace popular items than the active users.
Inspired by empirical analysis, we propose an evolving model for such networks,
in which the evolution is driven only by two-step random walk. Numerical
experiments verified that the model can qualitatively reproduce the
distributions of user activity and item popularity observed in empirical
networks. These results might shed light on the understandings of micro
dynamics of activity and popularity in social media networks.
