Simplicial models of social contagion

Abstract

Complex networks have been successfully used to describe the spread of diseases in populations of interacting individuals. Conversely, pairwise interactions are often not enough to characterize social contagion processes such as opinion formation or the adoption of novelties, where complex mechanisms of influence and reinforcement are at work. Here we introduce a higher-order model of social contagion in which a social system is represented by a simplicial complex and contagion can occur through interactions in groups of different sizes. Numerical simulations of the model on both empirical and synthetic simplicial complexes highlight the emergence of novel phenomena such as a discontinuous transition induced by higher-order interactions. We show analytically that the transition is discontinuous and that a bistable region appears where healthy and endemic states co-exist. Our results help explain why critical masses are required to initiate social changes and contribute to the understanding of higher-order interactions in complex systems.

Random walks on hypergraphs

“…Interestingly, more complicated nonlinear dynamics have been also recently studied on simplicial complexes [16,20,49,50] or in a pure multi-body frame [51]. Once again, however, the focus is placed on lowdimensional simplicial complexes (triangles).…”

“…Once again, however, the focus is placed on lowdimensional simplicial complexes (triangles). Recently, several dynamics, including epidemic spreading [16,49,52] and synchronisation [38], have been shown to produce new collective behaviours when higher-order interactions are assumed to shape the networked arrangement. In the projected network each hyperedge Eα becomes a complete clique of size |Eα|, with thus |Eα|(|Eα| − 1)/2 pairwise interactions.…”

Multibody interactions and nonlinear consensus dynamics on networked systems

“…Among those, multi-body models, sometimes called combinatorial models, focus on the importance of group interactions, that is situations when the basic unit of interaction involves more than two nodes. Multi-body interactions are observed in different areas in nature [2], society [3] and technology [4], with examples ranging from collaborations of authors [5] to neuronal activity [6,7]. Such systems may be represented as hypergraphs or simplicial complexes, and a substantial body of work has characterised their structural properties.…”

Toward epidemic thresholds on temporal networks: a review and open questions

“…Another key contribution was made by Zino et al (2016) who presented a continuous-time formulation of the problem. In recent work, Petri and Barrat (2018) and Iacopini et al (2019) have extended the activity driven model to higher-order interactions represented by so-called simplicial complexes. Prakash et al (2010b) examined the epidemic threshold under SIS dynamics for arbitrary temporal networks, represented by a sequence of T static network snapshots with adjacency matrices A = {A 1 , A 2 , .…”