Complex Social Contagions on Weighted Networks Considering Adoption Threshold Heterogeneity

Abstract

Many real-world phenomena can be described as complex contagions, which has attracted much attention in the field of network science. However, the effects of the heterogeneous adoption thresholds on complex contagions in weighted networks have not been systematically investigated. In this paper, we propose a heterogeneous complex contagion model on the weighted network, in which individuals have different adoption thresholds. For individuals with a relatively small adoption threshold, they are more likely to adopt the contagion and act as activists. An edge-weight based compartmental theory is developed to unveil spreading dynamics. Through extensive numerical simulations and theoretical analysis, we find that, for any weight distribution heterogeneity, with the increase of the activist fraction, the growth pattern of the final adoption size versus the information spreading probability changes from hybrid phase transition to a second-order continuous phase transition. Meanwhile, increasing the activist fraction can promote behavior spreading. Through bifurcation analysis, we discover that changing the heterogeneity of the weight distribution will not change the type of phase transition. Besides, reducing weight distribution heterogeneity can facilitate behavior spreading. Extensive numerical simulations verify that the theoretical solutions coincide with the numerical results very well. INDEX TERMS Complex contagions, heterogeneous adoption, weighted networks, threshold model, compartmental theory.

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“…However, using traditional data augmentation alone has defects, because repeated samples lead to over-sampling, which will easily lead to overfitting of the learning algorithm. To solve this problem, this study applies the weighted random sampling method to the overlapping of repeated samples, that is, the weight of each instance is defined by the number of instances in the class [32], and this weight represents the probability of the instance being randomly sampled [32], which can offset the oversampling effect of the class with a small number of samples. The weighted sampling method is based on weight Frontiers in Physics frontiersin.org sampling, which can reserve more labels and meet the diversity.…”

Effects of heterogeneous adoption thresholds on contact-limited social contagions

“…[44,45] Considering the non-Markovian nature of social contagions, many non-Markovian models with memory characteristic have been proposed in recent years. [33,[46][47][48][49][50][51][52][53][54][55] The research on social contagions with the reinforcement effect based on nonredundant information memory is receiving extensive attention from researchers. Based on the fact that the amount of information that an individual can provide is finite, the nonredundant information transmission method that only allows once successful information transmission between a pair of individuals is adopted.…”

“…However, heterogeneity is a topic of great interest for reflecting the ubiquitous inter-individual differences in real social systems. [47,[52][53][54][55]57,58] In some binary propagation threshold models, the adoption threshold in the population has two static values: equal to 1 and greater than 1, reflecting the high and low willingness to adopt the behavior. [47,52] Furthermore, some researchers set the adoption threshold of individuals to obey a certain probability distribution, which is more appropriate and reasonable than the binary threshold model to reflect the heterogeneity of adoption thresholds.…”