Life span in online communities

Recently online communities have attracted great interest and have become an important medium of information exchange between users. The aim of this work is to introduce a simple model of the evolution of online communities. This model describes (a) the time evolution of users' activity in a web service, e.g., the time evolution of the number of online friends or written posts, (b) the time evolution of the degree distribution of a social network, and (c) the time evolution of the number of active users of a web service. In the second part of the paper we investigate the influence of the users' lifespan (i.e., the total time in which they are active in an online community) on the process of rumor propagation in evolving social networks. Viral marketing is an important application of such method of information propagation.