Leah Keating (University of Limerick, Ireland)

Online Seminar – Join by using this link

Title: “A Multi-Type Branching Process Method for Modelling Complex Contagion on Clustered Networks”

Online social networks such as Twitter, Facebook, Instagram and TikTok serve as a medium for the spread of information between their users, we are interested in developing models for this information diffusion to gain a greater understanding of how it spreads. Some models for the spread of online behaviour and information assume that the information behaves similarly to the spread of 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 [1-2], 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 [3]; 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 account for the different numbers of active, inactive and removed nodes. This description allows for extensive Monte Carlo simulations (which are faster than network-based simulations), accurate analytical calculation of cascade sizes, determination of critical behaviour and other quantities of interest. For more information see our preprint on arXiv.

[1] D. Centola, The spread of behavior in an online social network experiment, Science 329, 1194 (2010).
[2] D. M. Romero, B. Meeder, and J. Kleinberg, Differences in the mechanics of information diffusion across topics: idioms, political hashtags, and complex contagion on twitter, in Proceedings of the 20th international conference on World wide web (2011) pp. 695–704.
[3] D. J. P. O’Sullivan, G. J. O’Keeffe, P. G. Fennell, and J. P. Gleeson, Mathematical modeling of complex contagion on clustered networks, Frontiers in Physics 3,10.3389/fphy.2015.00071 (2015).