The influence of heterogeneity of adoption thresholds on limited information spreading

doi:10.1016/j.amc.2021.126448

Applied Mathematics and Computation

Volume 411, 15 December 2021, 126448

https://doi.org/10.1016/j.amc.2021.126448 Get rights and content

Highlights

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The influence of adoption threshold heterogeneity on the process of information dissemination is studied in a two-layer network.
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The propagation model with limited contact is established.
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The threshold of information adoption is affected by the degree of node and a parameter obeying truncated normal distribution.
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Increasing the mean of parameters can inhibit information spreading and the effect of standard deviation of parameters on information dissemination depends on the mean of parameters.

Abstract

The spreading process of information on complex networks has been widely explored. In fact, different individuals in a network usually hold different standards for information adoption. Considering the heterogeneity of adoption thresholds, this study constructs a two-layer network model with limited contacts. The adoption threshold of a node is related to its degree and a parameter obeying truncated normal distribution. This study also proposes a partition theory based on edges to analyze the mechanism of information dissemination quantitatively. Experiments find that increasing the mean of parameters can inhibit information from spreading, and the effect of the standard deviation of parameters on information dissemination depends on the mean of parameters. For instance, when the mean of parameters is a low value, as the standard deviation of parameters increases, the information outbreak size will decrease. On the other hand, the information outbreak size will increase continuously with increased propagation probability. If the mean of parameters is high, the information outbreak size will increase first and then decrease with the increment in the standard deviation of parameters. The theoretical predictions of this study are in good agreement with the numerical simulations.

Introduction

With increasingly deepened social communication research, the study of the spreading dynamics on complex networks has become more meaningful. Many behaviors in the real world, such as advertising marketing [1], [2], social recommendation [3], [4], [5], healthy behavior [6], [7], [8], and public-opinion prevention and control [9], [10], can be explained by the theory of spreading dynamics. Different from epidemic spreading, social dynamics in complex networks has a reinforcement phenomenon [11], that is, individuals can accumulate the information they have received. When nodes accept social reinforcement from multiple neighbors in the network, the probability of individual adoption of behavior will increase. Centola et al. [12] proposed a linear propagation model for this mechanism, finding that this social communication process is non-Markov. On this basis, from the perspective of heterogeneity, researchers have studied the influence of nodes [13], [14], [15], community structures [16], dynamic network structures [17] and other factors on the spreading process. Information cascade [18] is also an important dynamic propagation process in complex networks, which can be used to describe the propagation dynamics of many behaviors. In order to facilitate the calculation, most of these studies are based on fixed adoption thresholds, that is, the conditions for each individual in the network to adopt information are the same. However, in fact, the adoption thresholds are affected by the heterogeneity of individuals. In other words, different individuals often have different standards for information adoption. For example, the adoption thresholds of information spreading may be affected by peoples age, educational level and religious belief.

Therefore, researchers have used some more complex threshold models. For instance, Zhu et al. [19] proposed a behavior adoption model with a tent-like adoption probability to analyze the ubiquitous local trend imitation characteristics. To approximate threshold-like behavior, Fink et al. [20] used a modified version of the logistic sigmoid function. Karampourniotis et al. [21] employed a truncated normal distribution of the nodes thresholds with a zero mean and explored the influence of standard deviation on cascade sizes. Peng et al. [22] explored the influence of the adoption thresholds obeying Gaussian distribution on the behavior propagation.

In addition, the existing studies show that the dissemination of information between individuals is usually limited. Restricted by time and space, individuals can only exchange information with others in a limited range [23], [24], [25], [26]. In social networks, for example, users cannot always keep in touch with all their friends [27]. In a scholar collaboration network, a scientist usually publishes papers together with only a few scholars in the short term [28], [29]. Wang et al. [30] constructed a behavior adoption mode to explore how the limited contacts affect social communications. Zhang et al. [31] proposed a partial interaction based propagation model, which assumes that informed individuals only contact with a certain part of their neighbors.

Considering the above factors, this proposes an adoption threshold heterogeneity model in a multilayer network, and then explores the influence of adoption threshold heterogeneity on the information dissemination process. Since many researchers choose to model on multi-layer networks [32], [33], [34], [35], this study uses a double-layer network model with limited propagation capacities. The adoption threshold of a node is related to its degree and a parameter obeying truncated normal distribution. This study also proposes a partition theory based on edge to analyze the mechanism of information dissemination quantitatively. It is found that increasing the mean of parameters can inhibit information from spreading and the effect of standard deviation of parameters on information dissemination depends on the mean of parameters. For a low mean of parameters, as the standard deviation of parameters increases, the information outbreak size will decrease. And this size will increase continuously with the increment in propagation probability. If the mean of parameters is large, the information outbreak size will increases first and then decreases with the increment in the standard deviation of parameters.

The central structure of this dissertation is as follows. In Section 2, a double-layer network information dissemination model based on heterogeneous adoption thresholds is constructed. Section 3 presents a partition theory based on edge to analyze the mechanism of information dissemination quantitatively. Section 4 describes the basic parameter settings of this study. Section 5 compares the experimental results obtained from the simulation experiment and theoretical derivation, with related phenomena analyzed. In Section 6, this study is summarized and some conclusions are drawn.

Section snippets

Information spreading model

First, we consider the underlying network model. In a double-layered network, each layer has $N$ nodes and the degree distribution of nodes is $P (k)$ . If nodes $i$ and $j$ have connected edges, they are neighbors. Then, we use an Susceptible-Adopted-Recovered (SAR) model based on the traditional SIR epidemic model to describe the information dissemination model. Every node in the network is in one of the three different states: susceptible (S), adopted (A), or recovered (R). In the S-state, nodes do

Theoretical analysis

Wang et al. [36] proposed a novel edge-based approach to estimate the outbreak spreading threshold and outbreak spreading size on networks. Based on this theory, we present a partition theory based on edge to theoretically analyze the influence of the heterogeneity of adoption thresholds on limited information dissemination. The proportion of recovery nodes at the end of the spreading process is used to represent the final information spreading size.

We assume that there exists a cavity state

Parameter settings

The number of nodes in the network is $10^{4}$ and average degree of nodes is $〈 k_{A} 〉 = 〈 k_{B} 〉 = 〈 k 〉 = 10$ . To validate our model, we adopt ER [38] network and SF [39] network as the infrastructure of communication network. We have carried out experiments on double-layer networks. The connection probability of any two nodes in ER network is the same, and the degrees of nodes obey Poisson distribution $p_{X} (k_{X}) = e^{- 〈 k_{X} 〉} \frac{{〈 k_{X} 〉}^{k_{X}}}{k_{X}!}$ in layer $X$ . Heterogeneity of nodes degree distribution is negatively correlated with the

Results and discussion

First, we consider the propagation on the double-layer ER network in Fig. 2. When the standard deviation approaches zero, the information outbreak size $R (\infty)$ versus the unit propagation probability $λ$ changes from discontinuous to continuous with different values of mean. When the standard deviation $δ = 0.1$ , $R (\infty)$ increases continuously with the increase of unit propagation probability $λ$ . This is because when the standard deviation approaches zero, the adoption threshold increases with the increase

Conclusions

In this paper, we propose an adoption thresholds heterogeneity model on a double-layer network to explore the influence of adoption thresholds heterogeneity on information spreading process. In order to quantitatively analyze the mechanism of information propagation, we also propose a partition theory based on edge. Through experiments, we find that increasing the mean of parameters can inhibit information spreading and the effect of standard deviation of parameters on information dissemination

Acknowledgments

This work was supported by Sub Project of National Key Research and Development plan in 2020(Grant No. 2020YFC1511704), Beijing Information Science & Technology University(NO.2020KYNH212, NO. 2021CGZH302), the National Natural Science Foundation of China (Grant No. 61971048) and Beijing Science and Technology Project (Grant No. Z191100001419012).

References (40)

Z. Wang et al.
Statistical physics of vaccination
Phys. Rep.
(2016)
S.-M. Cai et al.
Precisely identifying the epidemic thresholds in real networks via asynchronous updating
Appl. Math. Comput.
(2019)
Z.-K. Zhang et al.
Dynamics of information diffusion and its applications on complex networks
Phys. Rep.
(2016)
D. Centola et al.
Cascade dynamics of complex propagation
Physica A
(2007)
X. Zhu et al.
Dynamics of social contagions with local trend imitation
Sci. Rep.
(2018)
H. Peng et al.
Impact of the heterogeneity of adoption thresholds on behavior spreading in complex networks
Appl. Math. Comput.
(2020)
S. Boccaletti et al.
The structure and dynamics of multilayer networks
Phys. Rep.
(2014)
Y. Hu et al.
Bayesian personalized ranking based on multiple-layer neighborhoods
Inf. Sci. (Ny)
(2021)
A. Fiasconaro et al.
Hybrid recommendation methods in complex networks
Phys. Rev. E
(2015)
H. Yin et al.
Joint event-partner recommendation in event-based social networks
2018 IEEE 34th International Conference on Data Engineering (ICDE)
(2018)

P. Banerjee et al.

Maximizing welfare in social networks under a utility driven influence diffusion model

Proceedings of the 2019 International Conference on Management of Data

(2019)

X. Deng et al.

An influence model based on heterogeneous online social network for influence maximization

IEEE Trans. Netw. Sci. Eng.

(2019)

F. Xiong et al.

Exploiting implicit influence from information propagation for social recommendation

IEEE Trans. Cybern.

(2019)

H.-F. Zhang et al.

Suppressing epidemic spreading by imitating hub nodes strategy

IEEE Trans. Circuits Syst. II Express Briefs

(2019)

X.G. Chen et al.

Research on trend prediction and evaluation of network public opinion

Concurrenc. Comput.: Practic. Exp.

(2017)

Z. Yu et al.

Discovering information propagation patterns in microblogging services

ACM Trans. Know. Discov. Data (TKDD)

(2015)

D.-B. Chen et al.

Identifying influential spreaders in complex networks by propagation probability dynamics

Chaos: Interdiscip. J. Nonlinear Sci.

(2019)

S.-P. Pang et al.

Controllability limit of edge dynamics in complex networks

Phys. Rev. E

(2019)

F. Xiong et al.

Social recommendation with evolutionary opinion dynamics

IEEE Trans. Syst. Man Cybernetic.

(2020)

A. Nematzadeh et al.

Optimal network modularity for information diffusion

Phys. Rev. Lett.

(2014)

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View full text

The influence of heterogeneity of adoption thresholds on limited information spreading

Highlights

Abstract

Introduction

Section snippets

Information spreading model

Theoretical analysis

Parameter settings

Results and discussion

Conclusions

Acknowledgments

Phys. Rep.

Appl. Math. Comput.

Phys. Rep.

Physica A

Sci. Rep.

Appl. Math. Comput.

Phys. Rep.

Inf. Sci. (Ny)

Hybrid recommendation methods in complex networks

Phys. Rev. E

Joint event-partner recommendation in event-based social networks

2018 IEEE 34th International Conference on Data Engineering (ICDE)

Maximizing welfare in social networks under a utility driven influence diffusion model

Proceedings of the 2019 International Conference on Management of Data

An influence model based on heterogeneous online social network for influence maximization

IEEE Trans. Netw. Sci. Eng.

Exploiting implicit influence from information propagation for social recommendation

IEEE Trans. Cybern.

Suppressing epidemic spreading by imitating hub nodes strategy

IEEE Trans. Circuits Syst. II Express Briefs

Research on trend prediction and evaluation of network public opinion

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Discovering information propagation patterns in microblogging services

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Identifying influential spreaders in complex networks by propagation probability dynamics

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Phys. Rev. Lett.