AitF: Full: Collaborative Research: Modeling and Understanding Complex Influence in Social Networks

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Information, beliefs, diseases, technologies, and behaviors propagate through social interactions as a contagion. Understanding of how these contagions spread is crucial in encouraging beneficial and healthy behaviors and discouraging the ones that are destructive and damaging. Rigorous, mathematical understanding of complex social contagions is not just an abstraction, but will guide applications from healthcare to word-of-mouth advertising. The technical content of this project is inherently interdisciplinary, and its lessons will apply to related fields such as probability, economics, sociology, and statistical physics. The research efforts are integrated with the educational and outreach activities of the PIs, who have strong records of broadly disseminating cutting-edge research to high school, undergraduate, and graduate students through teaching, outreach programs, and personal mentoring. This project will transform our understanding of social contagions by: 1) Developing a suite of technical tools to enable improved understanding of specific complex processes; 2) Determining how various parameters of cascade and social structure together impact the chances of a cascade's success or failure; and 3) Obtaining empirical evidence to both corroborate the theoretical findings, and uncover the space of realistic setting for certain parameters. Many existing models of contagion assume that increasing the number of infected (or affected) neighbors marginally decreases the chance of infection. Many contagions, such as adoption of expensive new technology, fail to have this property, but instead have more complex rules for infection. This leads to different spreading behaviors even on the same networks. Motivated by sociology research findings, this project will greatly enhance our understanding of social contagions in three aspects. First this project will provide rigorous study of the spreading behavior of a simplified theoretical model called k-complex contagions and its interactions with structures in the underlying graph such as tie strength, unusually influential nodes, and community structures. Second, this project presents a general model for studying cascades that is both theoretically tractable and practically motivated. The general model generalizes most previous theoretical models of complex and simple contagions and includes homophily and environmental factors on cascades. Finally, this project will use post-hoc analysis as well as real world social experiments to verify the veracity of the model and fit the parameters in different settings.