  The engagement of each user in a social network is an essential indicator for
maintaining a sustainable service. Existing studies use the $coreness$ of a
user to well estimate its static engagement in a network. However, when the
engagement of a user is weakened or strengthened, the influence on other users'
engagement is unclear. Besides, the dynamic of user engagement has not been
well captured for evolving social networks. In this paper, we systematically
study the network dynamic against the engagement change of each user for the
first time. The influence of a user is monitored via two novel concepts: the
$collapsed~power$ to measure the effect of user weakening, and the
$anchored~power$ to measure the effect of user strengthening. We show that the
two concepts can be naturally integrated such that a unified offline algorithm
is proposed to compute both the collapsed and anchored followers for each user.
When the network structure evolves, online techniques are designed to maintain
the users' followers, which is faster than redoing the offline algorithm by
around 3 orders of magnitude. Extensive experiments on real-life data
demonstrate the effectiveness of our model and the efficiency of our
algorithms.
