Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen 2100-DK, Denmark.
Department of Mathematics, University of California, Los Angeles, California 90095, USA; Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom; and CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, United Kingdom.
Phys Rev E. 2019 Feb;99(2-1):022313. doi: 10.1103/PhysRevE.99.022313.
The spread of opinions, memes, diseases, and "alternative facts" in a population depends both on the details of the spreading process and on the structure of the social and communication networks on which they spread. One feature that can change spreading dynamics substantially is heterogeneous behavior among different types of individuals in a social network. In this paper, we explore how antiestablishment nodes (e.g., hipsters) influence the spreading dynamics of two competing products. We consider a model in which spreading follows a deterministic rule for updating node states (which indicate which product has been adopted) in which an adjustable probability p_{Hip} of the nodes in a network are hipsters, who choose to adopt the product that they believe is the less popular of the two. The remaining nodes are conformists, who choose which product to adopt by considering which products their immediate neighbors have adopted. We simulate our model on both synthetic and real networks, and we show that the hipsters have a major effect on the final fraction of people who adopt each product: even when only one of the two products exists at the beginning of the simulations, a small fraction of hipsters in a network can still cause the other product to eventually become the more popular one. To account for this behavior, we construct an approximation for the steady-state adoption fractions of the products on k-regular trees in the limit of few hipsters. Additionally, our simulations demonstrate that a time delay τ in the knowledge of the product distribution in a population, as compared to immediate knowledge of product adoption among nearest neighbors, can have a large effect on the final distribution of product adoptions. Using a local-tree approximation, we derive an analytical estimate of the spreading of products and obtain good agreement if a sufficiently small fraction of the population consists of hipsters. In all networks, we find that either of the two products can become the more popular one at steady state, depending on the fraction of hipsters in the network and on the amount of delay in the knowledge of the product distribution. Our simple model and analysis may help shed light on the road to success for antiestablishment choices in elections, as such success-and qualitative differences in final outcomes between competing products, political candidates, and so on-can arise rather generically in our model from a small number of antiestablishment individuals and ordinary processes of social influence on normal individuals.
意见、模因、疾病和“替代事实”在人群中的传播既取决于传播过程的细节，也取决于它们传播所依赖的社会和通信网络的结构。在社交网络中，不同类型的个体之间存在异质行为，这是一个可以极大改变传播动态的特征。在本文中，我们探讨了反建制节点（例如，潮人）如何影响两种竞争产品的传播动态。我们考虑了一种模型，其中传播遵循节点状态更新的确定性规则（表示已采用哪种产品），网络中可调概率 p_Hip 的节点是潮人，他们选择采用他们认为不那么受欢迎的两种产品之一。其余的节点是从众者，他们通过考虑直接邻居采用了哪种产品来选择采用哪种产品。我们在合成和真实网络上模拟了我们的模型，并表明潮人对最终采用每种产品的人数比例有重大影响：即使在模拟开始时只有两种产品中的一种存在，网络中的一小部分潮人仍然可以导致另一种产品最终成为更受欢迎的产品。为了说明这种行为，我们在很少有潮人的情况下，在 k-正则树上构造了产品的稳态采用分数的近似值。此外，我们的模拟表明，与最近邻居的产品采用情况的即时知识相比，人口中产品分布的知识的时间延迟τ对产品采用的最终分布有很大影响。使用局部树近似，我们推导出产品传播的解析估计值，如果人口中只有一小部分是潮人，则可以很好地吻合。在所有网络中，我们发现，如果网络中的潮人比例和产品分布知识的延迟量足够小，则任何一种产品都可以在稳态下成为更受欢迎的产品。我们的简单模型和分析可以帮助阐明反建制选择在选举中的成功之路，因为在我们的模型中，来自少数反建制个体和对普通个体的社会影响等普通过程，就可以相当普遍地产生成功——以及竞争产品、政治候选人等最终结果之间的定性差异。
