The concept of contagion has steadily expanded from its original grounding in epidemic disease to describe a vast array of processes that spread across networks, notably social phenomena such as fads, political opinions, the adoption of new technologies, and financial decisions. Traditional models of social contagion have been based on physical analogies with biological contagion, in which the probability that an individual is affected by the contagion grows monotonically with the size of his or her "contact neighborhood"-the number of affected individuals with whom he or she is in contact. Whereas this contact neighborhood hypothesis has formed the underpinning of essentially all current models, it has been challenging to evaluate it due to the difficulty in obtaining detailed data on individual network neighborhoods during the course of a large-scale contagion process. Here we study this question by analyzing the growth of Facebook, a rare example of a social process with genuinely global adoption. We find that the probability of contagion is tightly controlled by the number of connected components in an individual's contact neighborhood, rather than by the actual size of the neighborhood. Surprisingly, once this "structural diversity" is controlled for, the size of the contact neighborhood is in fact generally a negative predictor of contagion. More broadly, our analysis shows how data at the size and resolution of the Facebook network make possible the identification of subtle structural signals that go undetected at smaller scales yet hold pivotal predictive roles for the outcomes of social processes. social networks | systems S ocial networks play host to a wide range of important social and nonsocial contagion processes (1-8). The microfoundations of social contagion can, however, be significantly more complex, as social decisions can depend much more subtly on social network structure (9-17). In this study we show how the details of the network neighborhood structure can play a significant role in empirically predicting the decisions of individuals. We perform our analysis on two social contagion processes that take place on the social networking site Facebook: the process whereby users join the site in response to an invitation e-mail from an existing Facebook user (henceforth termed "recruitment") and the process whereby users eventually become engaged users after joining (henceforth termed "engagement"). Although the two processes we study formally pertain to Facebook, their details differ considerably; the consistency of our results across these differing processes, as well as across different national populations (Materials and Methods), suggests that the phenomena we observe are not specific to any one modality or locale. The social network neighborhoods of individuals commonly consist of several significant and well-separated clusters, reflecting distinct social contexts within an individual's life or life history (18) (19) (20) . We find that this multiplicity of social contexts, which we term structural diversity, plays a key role in predicting the decisions of individuals that underlie the social contagion processes we study. We develop means of quantifying such structural diversity for network neighborhoods, broadly applicable at many different scales. The recruitment process we study primarily features small neighborhoods, but the on-site neighborhoods that we study in the context of engagement can be considerably larger. For small neighborhoods, structural diversity is succinctly measured by the number of connected components of the neighborhood. For larger neighborhoods, however, merely counting connected components fails to distinguish how substantial the components are in their size and connectivity. To determine whether the structural diversity of on-site neighborhoods is a strong predictor of on-site engagement, we evaluate several variations of the connected component concept that identify and enumerate substantial structural contexts within large neighborhood graphs. We find that all of the different structural diversity measures we consider robustly predict engagement. For both recruitment and engagement, structural diversity emerges as an important predictor for the study of social contagion processes.
In REF , authors find that the probability of contagion is tightly controlled by the number of connected components in an individual's contacts neighborhood, rather than by the actual size of the neighborhood.
Structural diversity in social contagion
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Psychology Medicine Computer Science