Characterizing Information Diffusion in Online Social Networks with Linear Diffusive Model

Abstract—Mathematical modeling is an important approach to study information diffusion in online social networks. Prior studies have focused on the modeling of the temporal aspect of information diffusion. A recent effort introduced the spatio-temporal diffusion problem and addressed the problem with a theoretical framework built on the similarity between informa-tion propagation in online social networks and biological inva-sion in ecology [1]. This paper examines the spatio-temporal characteristics in further depth and reveals that there exist regularities in information diffusion in temporal and spatial dimensions. Furthermore, we propose a simpler linear partial differential equation that takes account of the influence of spatial population density and temporal decay of user interests in the information. We validate the proposed linear model with Digg news stories which received more than 3000 votes during June 2009, and show that the model can describe nearly 60 % of the news stories with over 80 % accuracy. We also use the most popular news story as a case study and find that the linear diffusive model can achieve an accuracy as high as 97:41 % for this news story. Finally, we discuss the potential applications of this model towards finding super spreaders and classifying news story into groups. Keywords-information diffusion, mathematical modeling, PDE, spatio-temporal, online social network. I