Patterns and modeling of group growth in online social networks

We investigate the group growth in online social networks, by analyzing six different user groups (two million users in total) in Douban Network. The size and longevity of posts in the Douban dataset demonstrate a power-law distribution with exponential cutoff and heavy tail, respectively. The frequency of user interactions follows a two-stage power-law distribution, which can distinguish different types of users. The growth of the number of users and the number of posts/replies generated by the users in a given and same time period, in each group, follow an exponential pattern at the initial stage and oscillate dramatically during the rest of the processes. The number of posts/replies has a power-law relation with the number of active users within a period of time. We propose an empirical growth model, Twisted Growth (TG), to portray the relation between the number of users and the amount of the contents they generated. The model derives equations based on the historical data for deciding coefficients, and the assumtion that the contents in one group will attract new users to join, which will lead to growth of users. Further, the newcomers together with original users will create new contents. We validate our TG model through theoretical analysis and simulations over real datasets.