Modeling of Information Diffusion on Social Networks with Applications to WeChat

Abstract: Traces of user activities recorded in online social networks such as the creation, viewing and forwarding/sharing of information over time open new possibilities to quantitatively and systematically understand the information diffusion process on social networks. From an online social network like WeChat, we could collect a large number of information cascade trees, each of which tells the spreading trajectory of a message/information such as which user creates the information and which users view or forward the information shared by which neighbors. In this work, we propose two heterogeneous non-linear models. Both models are validated by the WeChat data in reproducing and explaining key features of cascade trees. Specifically, we firstly apply the Random Recursive Tree (RRT) to model the cascade tree topologies, capturing key features, i.e. the average path length and degree variance of a cascade tree in relation to the number of nodes (size) of the tree. The RRT model with a single parameter $\theta$ describes the growth mechanism of a tree, where a node in the existing tree has a probability $d_i^{\theta}$ of being connected to a newly added node that depends on the degree $d_i$ of the existing node. The identified parameter $\theta$ quantifies the relative depth or broadness of the cascade trees, indicating that information propagates via a star-like broadcasting or viral-like hop by hop spreading. The RRT model explains the appearance of hubs, thus a possibly smaller average path length as the cascade size increases, as observed in WeChat. We further propose the stochastic Susceptible View Forward Removed (SVFR) model to depict the dynamic user behaviors including creating, viewing, forwarding and ignoring a message on a given social network.