Network robustness and irreversibility of information diffusion in Complex networks

Complex networks are characterized based on a newly proposed parameter, “degree of diffusion α”. 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 α such as the reverse diffusion (αreverse) and the random-kill-diffusion (RKD) processes. The analysis of αreverse 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.

► Complex networks are characterized based on the proposed “degree of diffusion α”. ► It defines the ratio of adopters to non-adopters within a diffusion process over penetration depths. ► The perfectness of a social network is evaluated by exploring the reverse diffusion and the random-kill-diffusion (RKD) processes. ► The analysis shows diffusion irreversibility in small-world and scale-free, and perfectness toward attacks in random networks. ► Furthermore, a real Complex network, represented as a “virtual friendship network” was characterized to be a randomized small-world network.