Fractional-Order Diffusion Model for Social Networks

Abstract

One of the most common areas of real world fractional-order model applications are diffusion processes. In the paper the attempt to use fractional-order diffusion equation to model information diffusion in a social network is made. The example dataset consist of citations for over 34000 arXiv papers. Basic diffusive fractional-order model is compared with Monte Carlo simulation of the flow of information from a particular node (paper) within the network. Experiments shown that the model of diffusion within network can be accurately fitted to the results obtained with the numerical method. Order of the obtained model (from 0.05 to 0.4 depending on the source node of diffusion) indicates, that the investigated citation network is a highly superdiffusive system. The results can be significant for the future works, including fractional-order generalization of epidemic models or diffusion in variable order networks.

Keywords: Social Network, Anomalous Diffusion, Fractional-Order Model