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Contagion on complex networks with persuasion.

Huang WM, Zhang LJ, Xu XJ, Fu X - Sci Rep (2016)

Bottom Line: Specifically, we study a combination of adoption and persuasion in cascading processes on complex networks.Finally, we study the effects of adoption and persuasion threshold heterogeneity on systemic stability.Though both heterogeneities give rise to global cascades, the adoption heterogeneity has an overwhelmingly stronger impact than the persuasion heterogeneity when the network connectivity is sufficiently dense.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, China.

ABSTRACT
The threshold model has been widely adopted as a classic model for studying contagion processes on social networks. We consider asymmetric individual interactions in social networks and introduce a persuasion mechanism into the threshold model. Specifically, we study a combination of adoption and persuasion in cascading processes on complex networks. It is found that with the introduction of the persuasion mechanism, the system may become more vulnerable to global cascades, and the effects of persuasion tend to be more significant in heterogeneous networks than those in homogeneous networks: a comparison between heterogeneous and homogeneous networks shows that under weak persuasion, heterogeneous networks tend to be more robust against random shocks than homogeneous networks; whereas under strong persuasion, homogeneous networks are more stable. Finally, we study the effects of adoption and persuasion threshold heterogeneity on systemic stability. Though both heterogeneities give rise to global cascades, the adoption heterogeneity has an overwhelmingly stronger impact than the persuasion heterogeneity when the network connectivity is sufficiently dense.

No MeSH data available.


Related in: MedlinePlus

Effect of heterogeneous thresholds on the cascade window in ER networks.Cascade windows on the (ϕ, z) plane with seed fraction ρ0 = 10−4 in the ER networks where the adoption threshold is normally distributed with a mean ϕ and a standard deviation σ = 0.1 (a) and the persuasion threshold is normally distributed with a mean ϕ′ = 0.5 and a standard deviation σ = 0.1 (b), respectively. The color codes represents analytical predictions of the final fraction of active nodes ρ based on Eq. (1). (c) Comparison of the cascade windows for both thresholds. The solid line corresponds to the result of Watts’ model with the uniform adoption threshold.
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f6: Effect of heterogeneous thresholds on the cascade window in ER networks.Cascade windows on the (ϕ, z) plane with seed fraction ρ0 = 10−4 in the ER networks where the adoption threshold is normally distributed with a mean ϕ and a standard deviation σ = 0.1 (a) and the persuasion threshold is normally distributed with a mean ϕ′ = 0.5 and a standard deviation σ = 0.1 (b), respectively. The color codes represents analytical predictions of the final fraction of active nodes ρ based on Eq. (1). (c) Comparison of the cascade windows for both thresholds. The solid line corresponds to the result of Watts’ model with the uniform adoption threshold.

Mentions: We now turn to the effect of the threshold heterogeneity on the cascade dynamics. Figure 6(a,b) show cascade windows for ER networks with the adoption and persuasion thresholds respectively following the Gaussian distribution. The standard deviation is σ = 0.1 representing fluctuations. For both cases, the active fraction increases with the network connectivity for a given ϕ inside the cascade window. Figure 6(c) shows the comparison of the cascade windows. It is clear that the threshold heterogeneity appears to increase the likelihood of global cascades. Especially for networks with dense connectivity, the adoption threshold has an overwhelming influence compared to that of the persuasion threshold. Such difference can be understood: when the persuasion threshold ϕ′ is Gaussian distributed, there is a higher probability for the active fraction of a adopter’s neighbors exceeds the persuasion threshold than the uniform case, which results in a stronger inducing effect on cascade propagation. While the network connectivity increases, an adopter is surrounded by many inactive neighbors, which leads to a lower chance for her to be a persuader. Hence the number of persuaders is reduced, leading to a less significant inducing effect. On the contrary, when the adoption threshold ϕ follows the Gaussian distribution, the increase of the network connectivity brings about more early adopters with lower adoption thresholds and relatively higher degrees, which accelerates cascade propagation. This conclusion is valid for a wider range of the seed fraction (see Supplementary Fig. S3).


Contagion on complex networks with persuasion.

Huang WM, Zhang LJ, Xu XJ, Fu X - Sci Rep (2016)

Effect of heterogeneous thresholds on the cascade window in ER networks.Cascade windows on the (ϕ, z) plane with seed fraction ρ0 = 10−4 in the ER networks where the adoption threshold is normally distributed with a mean ϕ and a standard deviation σ = 0.1 (a) and the persuasion threshold is normally distributed with a mean ϕ′ = 0.5 and a standard deviation σ = 0.1 (b), respectively. The color codes represents analytical predictions of the final fraction of active nodes ρ based on Eq. (1). (c) Comparison of the cascade windows for both thresholds. The solid line corresponds to the result of Watts’ model with the uniform adoption threshold.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4815014&req=5

f6: Effect of heterogeneous thresholds on the cascade window in ER networks.Cascade windows on the (ϕ, z) plane with seed fraction ρ0 = 10−4 in the ER networks where the adoption threshold is normally distributed with a mean ϕ and a standard deviation σ = 0.1 (a) and the persuasion threshold is normally distributed with a mean ϕ′ = 0.5 and a standard deviation σ = 0.1 (b), respectively. The color codes represents analytical predictions of the final fraction of active nodes ρ based on Eq. (1). (c) Comparison of the cascade windows for both thresholds. The solid line corresponds to the result of Watts’ model with the uniform adoption threshold.
Mentions: We now turn to the effect of the threshold heterogeneity on the cascade dynamics. Figure 6(a,b) show cascade windows for ER networks with the adoption and persuasion thresholds respectively following the Gaussian distribution. The standard deviation is σ = 0.1 representing fluctuations. For both cases, the active fraction increases with the network connectivity for a given ϕ inside the cascade window. Figure 6(c) shows the comparison of the cascade windows. It is clear that the threshold heterogeneity appears to increase the likelihood of global cascades. Especially for networks with dense connectivity, the adoption threshold has an overwhelming influence compared to that of the persuasion threshold. Such difference can be understood: when the persuasion threshold ϕ′ is Gaussian distributed, there is a higher probability for the active fraction of a adopter’s neighbors exceeds the persuasion threshold than the uniform case, which results in a stronger inducing effect on cascade propagation. While the network connectivity increases, an adopter is surrounded by many inactive neighbors, which leads to a lower chance for her to be a persuader. Hence the number of persuaders is reduced, leading to a less significant inducing effect. On the contrary, when the adoption threshold ϕ follows the Gaussian distribution, the increase of the network connectivity brings about more early adopters with lower adoption thresholds and relatively higher degrees, which accelerates cascade propagation. This conclusion is valid for a wider range of the seed fraction (see Supplementary Fig. S3).

Bottom Line: Specifically, we study a combination of adoption and persuasion in cascading processes on complex networks.Finally, we study the effects of adoption and persuasion threshold heterogeneity on systemic stability.Though both heterogeneities give rise to global cascades, the adoption heterogeneity has an overwhelmingly stronger impact than the persuasion heterogeneity when the network connectivity is sufficiently dense.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, China.

ABSTRACT
The threshold model has been widely adopted as a classic model for studying contagion processes on social networks. We consider asymmetric individual interactions in social networks and introduce a persuasion mechanism into the threshold model. Specifically, we study a combination of adoption and persuasion in cascading processes on complex networks. It is found that with the introduction of the persuasion mechanism, the system may become more vulnerable to global cascades, and the effects of persuasion tend to be more significant in heterogeneous networks than those in homogeneous networks: a comparison between heterogeneous and homogeneous networks shows that under weak persuasion, heterogeneous networks tend to be more robust against random shocks than homogeneous networks; whereas under strong persuasion, homogeneous networks are more stable. Finally, we study the effects of adoption and persuasion threshold heterogeneity on systemic stability. Though both heterogeneities give rise to global cascades, the adoption heterogeneity has an overwhelmingly stronger impact than the persuasion heterogeneity when the network connectivity is sufficiently dense.

No MeSH data available.


Related in: MedlinePlus