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Encapsulation Structure and Dynamics in Hypergraphs

21 marzo 2024
9:00 am
San Francesco Complex - Cappella Guinigi

Hypergraphs are a powerful modelling framework to represent systems where interactions may involve an arbitrarynumber of nodes. In this talk we will explore the extent to which smaller hyperedges are subsets of larger hyperedgesin real-world and synthetic hypergraphs, a property that we call encapsulation. Building on the concept of line graphs,we develop measures to quantify the relations existing between hyperedges of different sizes and, as a byproduct, thecompatibility of the data with a simplicial complex representation–whose encapsulation would be maximum. We thenturn to the impact of the observed structural patterns on diffusive dynamics, focusing on a variant of threshold models,called encapsulation dynamics, and demonstrate that non-random patterns can accelerate the spreading in thesystem.


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Timothy LaRock, Mathematical Institute, University of Oxford