Modelling Social Dynamics on Clustered Networks #

Leah Keating

12:10 Wednesday in 2Q49.

Part of the Networks and complex systems in society session.

Abstract #

Online social networks such as Twitter, Facebook, Instagram and TikTok serve as media for the spread of information between their users. We are interested in developing models for this information diffusion to gain a greater understanding of its drivers. Some models for the spread of online behaviour and information assume that the information behaves similarly to a virus, where infection is equally likely after each exposure, these dynamics are known as a simple contagion. In a simple contagion, the exposures are independent of each other. However, online adoption of some behaviour and content has been empirically observed to be more likely after multiple exposures from their network neighbours, the exposures are not independent of each other, we refer to this as a complex contagion. Analytically tractable descriptions of complex contagions have been developed for continuous-time dynamics. These extend mean-field and pair approximation methods to account for clustering in the network topologies; however, no such analogous treatments for discrete-time cascade processes exist using branching processes. We describe a novel definition of complex contagion adoption dynamics and show how to construct multi-type branching processes which account for clustering on networks. We achieve this by tracking the evolution of a cascade via different classes of clique motifs which contain different numbers of active, inactive and removed nodes. This description allows for accurate analytical calculation of cascade sizes, determination of critical behaviour and we also describe how the branching process description allows us, using probability generating functions, to derive full distributions of cascade sizes and other quantities of interest from the model.