Rumor spread in social network: Difference between revisions

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The spread of [[Rumor|rumors]] is an important form of [[communication]] in society. There are two approaches to investigateinvestigating the rumor spreading process: microscopic models and the macroscopic models. The macroscopic models propose a macro view about this process and are mainly based on the widely-used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks. By contrast, the microscopic models are more interested on micro-level interactions between individuals.

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The spread of [[Rumor|rumors]] is an important form of [[communication]] in society. There are two approaches to investigate the rumor spreading process: microscopic models and the macroscopic models. The macroscopic models propose a macro view about this process and are mainly based on the widely-used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks. By contrast, the microscopic models are more interested on micro-level interactions between individuals.

== Rumor propagation models ==

In the last few years, there has been a growing interest in rumor propagation in online social networks problems where different approaches have been proposed to investigate it. By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.

=== Macroscopic models ===

The first category is mainly based on the epidemic models. Pioneering research on rumor propagation using these models started during the 1960s.<ref name="DK">Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>

==== Epidemic models= ===

A standard model of rumor spreading was introduced by Daley and Kendall.<ref name=DK/> Assume there are N people in total and those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:

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the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.

==== Epidemic models in social networknetworks ====

We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. For all other <math>y</math>, <math>P(x,y)=0</math>.

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In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.

=== Microscopic models ===

The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."

The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models,<ref>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref> the energy model,<ref>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref> HISBmodel <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018.</ref> and Galam's Model.<ref>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>

==== Independent cascades models ====

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==== Linear threshold models ====

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==== Energy model ====

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==== HISBmodel model ====

The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.

The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.