Contagion in simplicial complexes

TL;DR

This paper investigates how information spreads in systems with complex, multi-component interactions modeled by simplicial complexes, revealing a phase transition that differs from traditional network models.

Contribution

It introduces a novel analysis of contagion dynamics in simplicial complexes, highlighting the role of higher-order interactions in spreading processes.

Findings

Higher order simplices dominate after initial spread

Discontinuous pandemic transition observed

Distinct phase diagram compared to traditional networks

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.