Network robustness and irreversibility of information diffusion in Complex networks

Complex networks are characterized based on a newly proposed parameter, “degree of diffusion ̨”. It defines the ratio of information adopters to non-adopters within a diffusion process over consecutive penetration depths. Furthermore, the perfectness of a social network is evaluated by exploring different variations of ̨ such as the reverse diffusion ( ̨reverse) and the random-kill-diffusion (RKD) processes. The analysis of ̨reverse and RKD processes shows information diffusion irreversibility in small-world and scale-free but not in random networks. It also shows that random networks are more stable toward attacks, resulting a complete information diffusion process over the entire network. Finally, a real Complex network example, represented as a “virtual friendship network” was analyzed and found to share properties of both random and small-world networks. Therefore, it is characterized to be somewhere between random and small-world network models or in other words, it is a randomized small-world network model. © 2011 Elsevier B.V. All rights reserved.