Nonlinear anomalous information diffusion model in social networks

Abstract

Modeling information diffusion in social networks is very important for predicting and controlling diffusions. Various types of diffusion models exist considering different properties of information diffusion. Recently it was shown that information diffusion in social networks like Digg and Twitter is anomalous, but it is not addressed in any information diffusion model. In this paper, a new mathematical information diffusion model is introduced based on anomalous diffusion characteristic that is not addressed before to the best of our knowledge. The proposed model is a nonlinear time-fractional Fisher's equation with Neumann boundary condition. The proposed model can model super-diffusion and sub-diffusion due to anomalous diffusion consideration. It is numerically solved using Haar wavelet and time discretization and validated with real datasets of Digg and Twitter social networks. The results show high precision in modeling the density of neighboring influenced users in time and space for different types and scales of diffusions. To predict non-neighbor influenced users, continuous-time random walk with jump is used with high precision. Combining the two models, the proposed nonlinear fractional diffusion model is a more realistic mathematical model and can model information diffusion in different types of social networks.