Increasing empirical evidence in recent years has shown that bots or malicious users in a social network play a critical role in the propagation of false information, while a theoretical modeling of such a problem has been largely ignored. In this paper, applying a simple contagion model, we study the effect of malicious nodes on the spreading of false information by incorporating the smart nodes who perform better than normal nodes in discerning false information. The malicious nodes, however, will always repost (or adopt) the false message as long as they receive it. We show analytically that, for a random distribution of malicious nodes, there is a critical number of malicious nodes above which the false information could outbreak in a random network. We further study three different distribution strategies of selecting malicious nodes for false information spreading. We find that malicious nodes that have large degrees, or are tightly connected, can enhance the spread. However, when they are close to the smart nodes, the spreading of false information can either be promoted or inhibited, depending on the network structure.
REFERENCES
1.
S.
Kumar
and N.
Shah
, “False information on web and social media: A survey,” arXiv:1804.08559 (2018).2.
S.
Vosoughi
, D.
Roy
, and S.
Aral
, “The spread of true and false news online
,” Science
359
, 1146
–1151
(2018
). 3.
S.
Funk
, E.
Gilad
, C.
Watkins
, and V. A. A.
Jansen
, “The spread of awareness and its impact on epidemic outbreaks
,” Proc. Natl. Acad. Sci. U.S.A.
106
, 6872
(2009
). 4.
Q.
Wu
, X.
Fu
, M.
Small
, and X.
Xu
, “The impact of awareness on epidemic spreading in networks
,” Chaos
22
, 013101
(2012
). 5.
Z.
Ruan
, M.
Tang
, and Z.
Liu
, “Epidemic spreading with information-driven vaccination
,” Phys. Rev. E
86
, 036117
(2012
). 6.
7.
M.
Karsai
, G.
Iñiguez
, K.
Kaski
, and J.
Kertész
, “Complex contagion process in spreading of online innovation
,” J. R. Soc. Interface
11
, 20140694
(2014
). 8.
G.
Iñiguez
, Z.
Ruan
, K.
Kaski
, J.
Kertész
, and M.
Karsai
, “Service adoption spreading in online social networks,” in Complex Spreading Phenomena in Social Systems (Springer, Cham, 2018), pp. 151–175.9.
A.
Gupta
, H.
Lamba
, P.
Kumaraguru
, and A.
Joshi
, “Faking Sandy: Characterizing and identifying fake images on Twitter during Hurricane Sandy,” in Proceedings of the 22nd International Conference on World Wide Web (Association for Computing Machinery, 2010), pp. 729–736.10.
Y.
Moreno
, R.
Pastor-Satorras
, and A.
Vespignani
, “Epidemic outbreaks in complex heterogeneous networks
,” Eur. Phys. J. B
26
, 521
(2002
). 11.
J.
Zhou
, Z.
Liu
, and B.
Li
, “Influence of network structure on rumor propagation
,” Phys. Lett. A
368
, 458
(2007
). 12.
Z.
Ruan
, P.
Hui
, H.
Lin
, and Z.
Liu
, “Risks of an epidemic in a two-layered railway-local area traveling network
,” Eur. Phys. J. B
86
, 13
(2013
). 13.
D. J.
Daley
and D. G.
Kendall
, “Stochastic rumours
,” J. Inst. Math. Appl.
1
, 42
(1965
). 14.
X.
Wang
, Y.
Lan
, and J.
Xiao
, “Anomalous structure and dynamics in news diffusion among heterogeneous individuals
,” Nat. Hum. Behav.
3
, 709
–718
(2019
). 15.
D. J.
Watts
, “A simple model of global cascades on random networks
,” Proc. Natl. Acad. Sci. U.S.A.
99
, 5766
(2002
). 16.
Z.
Ruan
, G.
Iñiguez
, M.
Karsai
, and J.
Kertész
, “Kinetics of social contagion
,” Phys. Rev. Lett.
115
, 218702
(2015
). 17.
Z.
Ruan
et al., “Effect of indirect social ties on cascading diffusion of information,” in Proceedings of International Workshop on Complex Systems and Networks (IWCSN) (IEEE, 2017), pp. 96–101.18.
W.
Huang
, L.
Zhang
, X.
Xu
, and X.
Fu
, “Contagion on complex networks with persuasion
,” Sci. Rep.
6
, 23766
(2016
). 19.
P.
Törnberg
, “Echo chambers and viral misinformation: Modeling fake news as complex contagion
,” PLoS One
13
, e02030958
(2018
). 20.
M.
Tambuscio
et al., “Fact-checking effect on viral hoaxes: A model of misinformation spread in social networks,” in Proceedings of the 24th International Conference on World Wide Web (Association for Computing Machinery, 2015), pp. 977–982.21.
Z.
Ruan
, J.
Wang
, Q.
Xuan
, C.
Fu
, and G.
Chen
, “Information filtering by smart nodes in random networks
,” Phys. Rev. E
98
, 022308
(2018
). 22.
Q.
Xuan
, X.
Shu
, Z.
Ruan
, J.
Wang
, C.
Fu
, and G.
Chen
, “A self-learning information diffusion model for smart social networks,” arXiv:1811.04362 (2018).23.
J. S.
Juul
and M. A.
Porter
, “Hipsters on networks: How a minority group of individuals can lead to an antiestablishment majority
,” Phys. Rev. E
99
, 022313
(2019
). 24.
H.
Allcott
and M.
Gentzkow
, “Social media and fake news in the 2016 election
,” J. Econ. Perspect.
31
, 211
–236
(2017
). 25.
D.
Li
et al., “Repetitive users network emerges from multiple rumor cascades,” arXiv:1804.05711 (2018).26.
C.
Shao
et al., “The spread of low-credibility content by social bots
,” Nat. Commun.
9
, 4787
(2018
). 27.
M.
Stella
, E.
Ferrara
, and M.
De Domenico
, “Bots increase exposure to negative and inflammatory content in online social systems
,” Proc. Natl. Acad. Sci. U.S.A.
115
, 12435
(2018
). 28.
29.
J.
Chen
et al., “GA-based Q-attack on community detection
,” IEEE Trans. Comput. Soc. Syst.
6
, 491
–503
(2019
). 30.
S.
Yu
et al., “Target defense against link-prediction-based attacks via evolutionary perturbations,” arXiv:1809.05912 (2018).31.
X.
Wang
et al., “Attack graph convolutional networks by adding fake nodes,” arXiv:1810.10751 (2018).32.
M. A.
Porter
and J. P.
Gleeson
, Dynamical Systems on Networks, Frontiers in Applied Dynamical Systems: Reviews and Tutorials Vol. 4 (Springer, 2016).33.
The asymptotic results will not be affected if using the asynchronous updating rule, where a single randomly selected node is updated in every time step; see the supplementary material.
34.
J. P.
Gleeson
and M. A.
Porter
, “Message-passing methods for complex contagions,” in Complex Spreading Phenomena in Social Systems (Springer, Cham, 2018), pp. 81–95.35.
V. S.
Subrahmanian
et al., “The DARPA Twitter bot challenge
,” IEEE Comput.
49
, 38
–46
(2016
). © 2020 Author(s).
2020
Author(s)
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