Modeling information diffusion in social networks with ordinary linear differential equations

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Nowadays, online social networks such as Twitter, Digg, and so on have become extremely popular thanks to the provision of unprecedented quantities of data to network users. This event has encouraged many studies of information diffusion in online social networks, especially in the mechanism and dynamics of the information diffusion process over such networks. Many previous studies of information diffusion in social networks have been based on experimental analyses or differential equations with temporal dimensions. Some recent studies have developed the information diffusion process using the heat transfer equations, the reaction–diffusion equations, or the hydrodynamic equations.This paper proposes a model called Ordinary Differential Information Diffusion or ODID to study both temporal and spatial patterns of the information diffusion process in online social networks. By using the formulation of ordinary differential equations, this model is constructed with friendship, relationships, and interactions between network users without quite relying on geometric linkages of the underlying network.The model is validated by the Digg data set whereby it is confirmed that with 95% confidence the ODID computations are not significantly different from the actual data and the average prediction accuracy of the model is about 98.78%.