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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 size of the giant component of inactive nodes ηc in ER networks.Symbols represent simulation results of the ER networks of size N = 104 and an average degree z = 3 (left column), 5 (middle column) and 10 (right column), respectively. The values of the persuasion threshold are ϕ′ = 0.8 (upper panel) and 0.6 (lower panel), respectively. Error bars are the standard deviations of the means. Lines are theoretical predictions by Eq. (6).
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f7: Effect of heterogeneous thresholds on the size of the giant component of inactive nodes ηc in ER networks.Symbols represent simulation results of the ER networks of size N = 104 and an average degree z = 3 (left column), 5 (middle column) and 10 (right column), respectively. The values of the persuasion threshold are ϕ′ = 0.8 (upper panel) and 0.6 (lower panel), respectively. Error bars are the standard deviations of the means. Lines are theoretical predictions by Eq. (6).

Mentions: Finally, we examine the threshold heterogeneity on the transition behaviour. Figure 7 shows the normalized size of the giant component of inactive nodes ηc as a function of the seed fraction ρ0 in ER networks. The upper and lower panels correspond to ϕ′ = 0.8 and 0.6, respectively. When the network connectivity is sufficiently sparse (z = 3) and the persuading effect is sufficiently weak (ϕ′ = 0.8), the system exhibits the continuous transition for σ = 0 (see Fig. 7(a)). When the adoption heterogeneity is allowed but of a relatively small value (σϕ = 0.1), the transition becomes discontinuous. For larger adoption heterogeneity (σϕ = 0.2) the system exhibits the continuous transition again. This is qualitatively the same as the ϕ-threshold model38. On the contrary, the increase of the persuasion heterogeneity σϕ′ results in the monotonic change in the phase transition: the transition is always discontinuous in dense networks or in networks with strong persuasion (see Fig. 7(b–f)).


Contagion on complex networks with persuasion.

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

Effect of heterogeneous thresholds on the size of the giant component of inactive nodes ηc in ER networks.Symbols represent simulation results of the ER networks of size N = 104 and an average degree z = 3 (left column), 5 (middle column) and 10 (right column), respectively. The values of the persuasion threshold are ϕ′ = 0.8 (upper panel) and 0.6 (lower panel), respectively. Error bars are the standard deviations of the means. Lines are theoretical predictions by Eq. (6).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f7: Effect of heterogeneous thresholds on the size of the giant component of inactive nodes ηc in ER networks.Symbols represent simulation results of the ER networks of size N = 104 and an average degree z = 3 (left column), 5 (middle column) and 10 (right column), respectively. The values of the persuasion threshold are ϕ′ = 0.8 (upper panel) and 0.6 (lower panel), respectively. Error bars are the standard deviations of the means. Lines are theoretical predictions by Eq. (6).
Mentions: Finally, we examine the threshold heterogeneity on the transition behaviour. Figure 7 shows the normalized size of the giant component of inactive nodes ηc as a function of the seed fraction ρ0 in ER networks. The upper and lower panels correspond to ϕ′ = 0.8 and 0.6, respectively. When the network connectivity is sufficiently sparse (z = 3) and the persuading effect is sufficiently weak (ϕ′ = 0.8), the system exhibits the continuous transition for σ = 0 (see Fig. 7(a)). When the adoption heterogeneity is allowed but of a relatively small value (σϕ = 0.1), the transition becomes discontinuous. For larger adoption heterogeneity (σϕ = 0.2) the system exhibits the continuous transition again. This is qualitatively the same as the ϕ-threshold model38. On the contrary, the increase of the persuasion heterogeneity σϕ′ results in the monotonic change in the phase transition: the transition is always discontinuous in dense networks or in networks with strong persuasion (see Fig. 7(b–f)).

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