Diffusion of information, behavioral patterns or innovations follows diverse pathways depending on a number of conditions, including the structure of the underlying social network, the sensitivity to peer pressure and the influence of media Here we study analytically and by simulations a general model that incorporates threshold mechanism capturing sensitivity to peer pressure, the effect of "immune" nodes who never adopt, and a perpetual flow of external information While any constant, nonzero rate of dynamically introduced spontaneous adopters leads to global spreading, the kinetics by which the asymptotic state is approached shows rich behavior In particular, we find that, as a function of the immune node density, there is a transition from fast to slow spreading governed by entirely different mechanisms This transition happens below the percolation threshold of network fragmentation, and has its origin in the competition between cascading behavior induced by adopters and blocking due to immune nodes This change is accompanied by a percolation transition of the induced clusters

Kinetics of Social Contagion

Real social contagion processes usually accompany feedback behaviors, such as people may give comments after they adopt a new product or watch a new movie, etc. In this paper, we extend the traditional threshold model that has been widely adopted for studying social contagion phenomena by incorporating the negative-feedback mechanism. In our model, nodes may give negative feedbacks with a certain probability after they become adopters, and correspondingly, the threshold of their susceptible neighbors will increase. By extensive simulations and mean-field analysis, we find that, if nodes give negative feedbacks with high possibility immediately after they become adopters, the contagion process could be effectively suppressed with only slight disturbances to the system, i.e., only a small fraction of nodes give negative feedbacks finally. • We extend the traditional threshold model by incorporating the negative-feedback mechanism. • A mean-field method is applied to analyze the proposed model. • The results provide some insights into the social contagion phenomena in reality. 

Social contagion with negative feedbacks

As social networks play an increasingly important role in people's lives, people are more likely to discuss hot topics on social networks. Predicting the spread of hot topics, known as topic propagation prediction is an important task. Due to the unpredictability of the users and topics in social networks, predicting the topic propagation trend is still a major challenge. Different users play different roles in topic propagation. However, existing studies have not utilized user role analysis. In this paper, we propose a topic propagation prediction method (TPP) based on user role analysis and dynamic probability model. First, we describe our user role analysis, which incorporates four user-factors to characterize user attributes along two dimensions. Second, we combine dynamic probability model with user role analysis to accurately predict the topic propagation trend. Finally, we prove the efficiency of TPP by experiments.

/pdf/topic-propagation-prediction-based-on-dynamic-probability-3r35fp5o6t.pdf

Topic Propagation Prediction Based on Dynamic Probability Model

The invention relates to a social stratification model implementation method based on network information stream, which comprises the following steps of: S1: leading in a network; S2: selecting an intelligent node, and assuming that the overall network has and only has one intelligent node; S3: initializing weights, and allocating one fixed constant to each directed connected edge weight in the network; S4: by propagating true and false messages on the basis of cascading information, traversing each common node in the network, repeatedly circulating, and finally, carrying out statistics on anaverage number of the true and false messages forwarded by the overall network when each common node is used as a source node; and S5: calculating network social stratification model indexes which comprise a true message information diffusion ability difference value and a false message information diffusion ability difference value. When the social network has the intelligent node, the true and false message propagating number can have a social stratification phenomenon in the overall network. The invention provides the social stratification model implementation method based on the network information stream. Such model can help a researcher to better know a mechanism of generating the social stratification phenomenon in the network and effects of the intelligent node.

Social stratification model implementation method based on network information stream

Watts model is a classic paradigm for studying social contagion phenomena. In prior research, the decision threshold of an individual is independent of its neighbors’ states. In this paper, we extend the Watts model by introducing the positive-feedback mechanism. In our model, each adopter may give positive feedbacks with a certain probability. Correspondingly, the threshold of its susceptible neighbors will decrease by a small number. We perform extensive numerical simulations on synthetic networks and an empirical social network, and demonstrate that positive feedbacks could significantly facilitate the contagion process. Furthermore, we find that network heterogeneity plays a complex role in the cascading dynamics. 

The Role of Positive Feedbacks in the Watts Model

Diffusion of commercial products, ideas or innovations are all examples of information cascade, where a small initial shock may trigger a global cascade. One assumption usually adopted by researchers is the threshold mechanism, which assumes that a person will convert its state (from inactive to active) if a certain fraction of its neighbors has done so. In the original threshold model, only the direct neighbors of a node participate in the decision making of that person. However, increasingly empirical studies show that the indirect social ties are also of importance in many aspects in real life. Here we study how these indirect social ties affect the information cascading process. Motivated by the real situation, we assume a fraction r of nodes is in immune state, which can not be influenced by others. We perform simulations on both random ER and community networks, and find that without immune nodes the indirect social ties play an inhibitory role in the information cascading process. However, as r increases, the existence of indirect social ties may also facilitate the spreading process to some extent.

Effect of indirect social ties on cascading diffusion of information

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Effect of indirect social ties on cascading diffusion of information