Information Diffusion Structure on Social Networks with General Degree Distribution

In this paper, we study the information diffusion structure on social networks with general degree distribution. To describe the information diffusion structure, we adopt six different viewpoints of metrics, including structural virality, distance variance, distance variability, distance susceptibility, cascade depth and cascade width. On Erdös–Rényi (ER) networks, we can intuitively see that as the diffusion tree becomes denser, the depth of the diffusion tree first increases to a peak and then decreases with the infection rate increasing, in addition the distance distribution of the diffusion tree obeys exponential distribution, and the metrics except cascade width decrease after reaching their peak values. When the information diffuses on scale-free (SF) networks, the diffusion trees are similar with the ones on ER networks. In other words, compared with the degree distribution, the infection rate is the main factor of diffusion tree in the same network scale.