Hipsters on networks: How a minority group of individuals can lead to an antiestablishment majority.

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.