Fig 1.
The diffusion trees in LJ community.
a, a real instance of information diffusion. An illustration of a diffusion tree containing 227 nodes which reaches the depth of 8. Each node represents a post published in LJ community, whereas each link stands for a spreading instance. The node color indicates the depth of a node in the diffusion tree. The size of a node is proportional to the number of its children. The links of social spreading, self-promotion, and broadcast are represented by the colors of red, grey, and blue respectively. b shows the probability distributions of diffusion trees’ size and depth. Both the tree size and depth exhibit approximately pow-law distributions. The power-law exponents for tree size and depth are γs = 1.86 ± 0.05 and γd = 2.97 ± 0.29 respectively. The straight lines represent the maximum likelihood fitting of the data points.
Fig 2.
a shows the probability distributions of the size of diffusion trees and viral spreading processes. The inset displays the distributions of spreading depth for both cases. The straight lines are fitted with the maximum likelihood method. In b, we present the proportion of diffusion instances in spreading processes with a given depth. The relation between the size of viral spreading and diffusion trees is displayed in c. Error bars indicate the 10% and 90% percentiles. The inset presents the diminishing ratio when mapping the diffusion trees to viral spreading. In d, we classify the nodes according to their depth in spreading processes and display their average branching number.
Fig 3.
SIR modeling with users’ infection rate cannot reproduce the realistic viral spreading pattern.
a, distribution of the real-world infection rate for each individual β calculated from viral spreading instances. We display the ratio between the size distribution of SIR simulations and real viral spreading in b. Inset shows the ratio of depth distribution. In c, we present the proportion of diffusion trees with a given depth for both SIR simulations and real viral spreading, and show the ratio between real cases and SIR modeling in the inset. d presents the proportion of spreading instances for diffusion with a specific depth for both cases. The inset shows the ratio between real viral spreading and simulations. In e and f, we perform same analyses for viral spreading without interactions with other diffusion types.
Fig 4.
SIR modeling with links’ infection rate cannot reproduce the realistic viral spreading pattern.
a, distribution of the real-world infection rate for each social link β calculated from viral spreading instances. The ratio between the size distribution of SIR simulations and real viral spreading is displayed in b. Inset shows the ratio of depth distribution. In c, the proportion of diffusion trees with a given depth for both SIR simulations and real viral spreading is presented, and the ratio between real cases and SIR modeling is shown in the inset. d illustrates the proportion of spreading instances for diffusion with a given depth for both cases. The inset shows the ratio between real viral spreading and simulations. Same analyses are shown in e and f for real viral spreading without interactions with self-promotion and broadcast diffusion.
Fig 5.
Analysis of the self-promotion.
a shows the distributions of the size and depth of self-promotion diffusion trees. The fraction of self-promotion links in diffusion trees with a certain depth is displayed in b. In c we present the probability distribution of the total number of self-promotion for each user, which has a power-law shape with exponent γ = 1.62 ± 0.08. In d we plot the relationship between posts’ branching number and their depth in self-promotion diffusion trees.
Fig 6.
In a, we display the distributions of the size and depth for broadcast diffusion trees and broadcast spreading respectively. The proportion of broadcast links in diffusion processes with a certain depth is shown in b. The relation between the size of broadcast spreading and broadcast diffusion trees is displayed in c. Error bars indicate 10% and 90% percentiles. The inset presents the diminishing ratio when mapping the diffusion trees to broadcast spreading. We plot nodes’ average branching number versus their depth in diffusion in d.
Fig 7.
The human activity of LJ users.
In a we show the distribution of users’ activity for each mechanism. For each user, we calculate the fraction of each mechanism that the selected user has conducted, and present the distribution of obtained fraction in b. In the inset we change the linear scale of y axis to a logarithmic scale. c displays the distribution of response time τ for social spreading, self-promotion, and broadcast. We adopt the time unit of second in the main panel and day in the inset.
Fig 8.
Coupling of distinct mechanisms.
We plot the fraction of the social spreading, self-promotion, and broadcast links in diffusion trees deeper than a given threshold in a. The x-axis value is the lower bound of selected trees’ depth. In b, the distribution of the route number for each type is displayed. We calculate the average route number of the diffusion links for each type in diffusion trees deeper than a certain depth, and present the results in c. After removing the leaves of diffusion trees, we obtain the information diffusion skeletons. We show the average route number and composition in diffusion skeletons whose depth exceeds certain values in the main panel and inset of d respectively. In the spreading processes among population, the fraction and average route number of social spreading and broadcast links are presented in e and f.
Fig 9.
The average route number versus response time for different mechanisms.
For each diffusion type, we classify diffusion links according to their response time (in second), or equivalently the diffusion speed, and display the average route number for each case.