Contagion in simplicial complexes
arXiv:2107.03411 · doi:10.1016/j.chaos.2021.111307
Abstract
The propagation of information in social, biological and technological systems represents a crucial component in their dynamic behavior. When limited to pairwise interactions, a rather firm grip is available on the relevant parameters and critical transitions of these spreading processes, most notably the pandemic transition, which indicates the conditions for the spread to cover a large fraction of the network. The challenge is that, in many relevant applications, the spread is driven by higher order relationships, in which several components undergo a group interaction. To address this, we analyze the spreading dynamics in a simplicial complex environment, designed to capture the coexistence of interactions of different orders. We find that, while pairwise interactions play a key role in the initial stages of the spread, once it gains coverage, higher order simplices take over and drive the contagion dynamics. The result is a distinctive spreading phase diagram, exhibiting a discontinuous pandemic transition, and hence offering a qualitative departure from the traditional network spreading dynamics.
arXiv comment7 pages and 6 figures
References in corpus (14)
- The structure and function of complex networks
- Epidemic spreading in scale-free networks
- Epidemic processes in complex networks
- Networks beyond pairwise interactions: structure and dynamics
- Higher-order organization of complex networks
- Simplicial models of social contagion
- Epidemic spreading in correlated complex networks
- Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks
- Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
- Dynamic Effects Increasing Network Vulnerability to Cascading Failures
- Network Geometry
- Abrupt phase transition of epidemic spreading in simplicial complexes
- Growing scale-free simplices
- Network Geometry and Complexity