Traces of user activities recorded in online social networks open new possibilities to systematically understand the information diffusion process on social networks. From the online social network WeChat, we collected 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, one for the topologies of the information cascade trees and the other for the stochastic process of information diffusion on a social network. Both models are validated by the WeChat data in reproducing and explaining key features of cascade trees.
Specifically, we apply the Random Recursive Tree (RRT) to model the growth of cascade trees. The RRT model could capture 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. Its single identified parameter quantifies the relative depth or broadness of the cascade trees and indicates 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 behavior including creating, viewing, forwarding and ignoring a message on a given social network. Beside the average path length and degree variance of the cascade trees in relation to their sizes, the SVFR model could further explain the power-law cascade size distribution in WeChat and unravel that a user with a large number of friends may actually have a smaller probability to read a message (s)he receives due to limited attention.@en

Online social networks can detailedly and accurately record the activities of human beings and the trajectories of information dissemination over time, which provides us an opportunity to understand the information diffusion process from a renewed, more realistic, data driven modeling dimensionality. In consideration of two fundamental behaviors (viewing and sharing) involved in information diffusion, we propose a stochastic, heterogeneous, continuous-time delay Unknown-View-Share-Removed (UVSR) model to characterize the information diffusion process. The UVSR model introduces four parameters to describe the diffusion probability and speed: viewing/sharing probability/delay. These parameters are subject to some sort of distributions from the actual data, or based on empirical assumptions. To validate the model, we collect and analyze large number of information cascades (tree structure) diffused in WeChat network. We find that the viewing delay and sharing delay are approximately subject to log-normal and power-law distributions respectively, and the sharing probability follows a Gaussian distribution. Driven by these empirical findings and a constant viewing probability assumption, our model can reproduce numerous key features of information diffusion process in both topology and temporal dynamics, such as cascade size distribution, structural virality, life span distribution and relative propagation speed. Our work contributes to a better understanding of the topological features and temporal dynamics of information diffusion from a continuous time, stochastic modeling view.

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