Beyond the common network representation: a Simplicial Activity Driven model

The use of a network representation has become commonplace for describing and studying a large number of complex systems: the elements of the systems are seen as nodes, and links between nodes represent pairwise interactions. For many biological and social systems, however, elementary interactions involve more than two elements, and simplicial complexes are more adequate to describe such phenomena.

In a new paper just published in Physical Review Letters, ISI Foundation Research Leader Giovanni Petri and ISI Senior Researcher Alain Barrat propose a framework to model such an evolution: the simplicial activity driven model, in which the building block is a simplex of nodes representing a multiagent interaction.

Researchers show analytically and numerically that the use of simplicial structures leads to crucial structural differences with respect to the activity driven model, a paradigmatic temporal network model involving only binary interactions. It also impacts the outcome of paradigmatic processes modeling disease propagation or social contagion (fluctuations in the number of nodes involved in the interactions can affect the outcome of models of simple contagion processes, contrarily to what happens in the activity driven model).

“Simplicial Activity Driven model”, Giovanni Petri and Alain Barrat, Physical Review Letters, 29th Novembre 2018. Link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.228301