The Effect of Heterogeneity on Hypergraph Contagion Models


November 19, 2020

I’m excited to share my work with Juan Restrepo titled “The effect of heterogeneity on hypergraph contagion models”! We found that the heterogeneity of pairwise and group interactions strongly affects the appearance of “tipping point” behavior and you can find the paper in Chaos or on ArXiV. Deciphering the jargon: A hypergraph is a mathematical structure that allows us to represent not only individual interactions but group interactions as well (Illustration below).

An illustration of a hypergraph

Contagion models are well-studied on pairwise networks, but lately, researchers have been interested in the effect of including group interactions. We know that often ideas or opinions can become viral or die out, depending on whether they reach a “critical mass”. This is often called “tipping point” behavior. A contagion in our study could mean an opinion, a virus, a meme, etc. – just something that you would pass on to your friends or friend groups. See Malcom Gladwell’s book, “The Tipping Point” for some neat examples.

Iacopo Iacopini et al. showed in Simplicial Models of Social Contagion that extending the network SIS model to include group interactions can induce tipping point behavior. We extended this idea to explore the effect of heterogeneity in the contact structure both through individual and group connections. We looked at several different pairwise degree distributions and two different ways to connect nodes in groups of three. We observed that a more heterogeneous contact structure (read: closer to real-world social networks) in your individual connections makes tipping points less likely and more heterogeneity in the number of group connections tends to make tipping points more likely. One way to think about this is that there are two competing infection mechanisms. Pairwise transmissions lead to continuous transitions, whereas group transmissions lead to tipping point behavior. Depending on which of these pathways dominate determines the behavior observed. My code is freely available on Github, there is a press release here and again the article is in Chaos or on ArXiV. Reach out to me if you are interested in chatting more!