Abstract
In the realistic world, various individuals have distinct personalities, preferences, and attitudes toward new information and behavior acceptance, called population heterogeneity. It is seldom taken into account and theoretically analyzed in information propagation on a weighted network. Therefore, we divide individuals into fashionable and conservative individuals according to their passion degree and willingness for novel behaviors acceptance. Then, we build two behavior adoption threshold models corresponding to fashionable and conservative individuals on the weighted network to explore the effect of population heterogeneity on information propagation. Next, a partition theory based on edge weight and population heterogeneity is proposed to qualitatively analyze the information propagation mechanism. The theoretical analyses and simulation results show that fashionable individuals promote information propagation and behavior adoption. More importantly, the crossover phenomena of phase transition appear. When the fraction of fashionable individuals is relatively large, the increasing pattern of the final adoption size shows a second-order continuous phase transition. In comparison, the increasing pattern alters to first-order discontinuous phase transition with the decrease of the fraction of fashionable individuals. Moreover, reducing weight distribution heterogeneity promotes information propagation and slightly accelerates the change of the phase transition pattern from the first-order discontinuous to the second-order continuous. Besides, increasing the degree distribution heterogeneity accelerates the change of the phase transition pattern. Finally, our theoretical analyses coincide well with the simulation results.
Highlights
With the rapid development of fifth-generation mobile communication technology and intelligent mobile terminals, social networks are increasingly significant in people’s lives, such as Facebook, Twitter, WeChat, Microblog, and other social software [1–4]. e information propagation between users plays an increasingly significant role in social networks, which provides great convenience for people’s work and life [5, 6]. e information propagation theory can be utilized to explain many behaviors in widespread reality application fields, such as social recommendation [7, 8], information fraud [9], health [10–12], and advertising marketing [13].In recent years, researchers have conducted in-depth studies for information propagation models in terms of theoretical analyses and experimental models [14] and explored many potential factors influencing the information propagation mechanisms, such as node distribution structures [7, 15, 16], node contact preference [17], memory effects [18, 19], and heterogeneous adoption thresholds [20, 21].Massive studies revealed that information propagation exhibits social affirmation or reinforcement due to the multiple confirmations of the credibility and legitimacy of the behavior information [17, 22]
To describe the social reinforcement, the threshold model based on the nonMarkov process is one of the classic models, in which individual behavior adoption exhibits memory effects [17, 23]
En we introduce the edge-weight distribution to reflect the edges heterogeneity. e edge weight between two adjacent nodes i and j is denoted by ωij, and the edge-weight distribution by a function f(ω). e probability that an susceptible state (S-state) node j receives the information from its adopted state (A-state) neighbor node i is denoted by the following equation: λω λωij 1 − (1 − β)ωij, (1)
Summary
With the rapid development of fifth-generation mobile communication technology and intelligent mobile terminals, social networks are increasingly significant in people’s lives, such as Facebook, Twitter, WeChat, Microblog, and other social software [1–4]. e information propagation between users plays an increasingly significant role in social networks, which provides great convenience for people’s work and life [5, 6]. e information propagation theory can be utilized to explain many behaviors in widespread reality application fields, such as social recommendation [7, 8], information fraud [9], health [10–12], and advertising marketing [13].In recent years, researchers have conducted in-depth studies for information propagation models in terms of theoretical analyses and experimental models [14] and explored many potential factors influencing the information propagation mechanisms, such as node distribution structures [7, 15, 16], node contact preference [17], memory effects [18, 19], and heterogeneous adoption thresholds [20, 21].Massive studies revealed that information propagation exhibits social affirmation or reinforcement due to the multiple confirmations of the credibility and legitimacy of the behavior information [17, 22]. To explore the influence of population heterogeneity on the information propagation mechanism, we construct a weighted social network model with N individuals and degree distribution P(k).
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