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.

翻译：每个用户在社会网络中的参与是维持可持续服务的基本指标。现有的研究使用用户的美元份额来精确估计其在网络中的静态参与。然而,当用户的参与被削弱或加强时,对其他用户的参与的影响就不清楚。此外,用户参与的动态对于不断演变的社会网络并没有很好地捕捉到。在本文件中,我们系统研究网络的动态以对抗每个用户的首次参与变化。一个用户的影响力通过两个新概念来监测:用美元折叠~功率来衡量用户削弱的影响,用$ancrored~power$来衡量用户加强影响。我们表明,这两个概念可以自然地结合,这样可以提出统一的离线算法,为每个用户既计算崩溃的追随者又计算固定的追随者。在网络结构演变时,网上技术旨在维持用户的追随者,这比用大约3级重编离线算法的速度要快。关于实际生活数据的广泛实验显示了我们模型的有效性和我们算法的效率。