Markov-based solution for information diffusion on adaptive social networks

There is currently growing interest in modeling the information diffusion on social networks across multi-disciplines, including the prediction of the news popularity, the detection of the rumors and the influence of the epidemiological studies. Following the framework of the epidemic spreading, the information spreading models assume that information can be transmitted from the known individuals (infected) to the un-known individuals (susceptible) through the network interactions. During this process, individuals also always change their interactions which in turn will greatly influence the information spreading. In this work, we propose a mechanism considering the co-evolution between information states and network topology simultaneously, in which the information diffusion was executed as an SIS process and network topology evolved based on the adaptive assumption. The theoretical analyses based on the Markov approach were very consistent with simulation. Both simulation results and theoretical analyses indicated that the adaptive process, in which informed individuals would rewire the links between the informed neighbors to a random non-neighbor node, can enhance information diffusion (leading to much broader spreading). In addition, we obtained that two threshold values exist for the information diffusion on adaptive networks, i.e., if the information propagation probability is less than the first threshold, information cannot diffuse and dies out immediately; if the propagation probability is between the first and second threshold, information will spread to a finite range and die out gradually; and if the propagation probability is larger than the second threshold, information will diffuse to a certain size of population in the network. These results may shed some light on understanding the co-evolution between information diffusion and network topology.