https://doi.org/10.1140/epjds/s13688-024-00490-1
Research
The structural evolution of temporal hypergraphs through the lens of hyper-cores
1
Aix-Marseille Univ, Université de Toulon, CNRS, CPT, Turing Center for Living Systems, 13009, Marseille, France
2
Network Science Institute, Northeastern University London, E1W 1LP, London, United Kingdom
3
Department of Physics, Northeastern University, 02115, Boston, MA, USA
4
NP Lab, Network Science Institute, Northeastern University London, E1W 1LP, London, United Kingdom
5
CENTAI, Corso Inghilterra 3, 10138, Turin, Italy
a
marco.mancastroppa@cpt.univ-mrs.fr
Received:
19
February
2024
Accepted:
12
July
2024
Published online:
25
July
2024
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the behaviour of the system itself. An adequate description of these systems is offered by temporal hypergraphs, that integrate these features within the same framework. However, tools for their temporal and topological characterization are still scarce. Here we develop a series of methods specifically designed to analyse the structural properties of temporal hypergraphs at multiple scales. Leveraging the hyper-core decomposition of hypergraphs, we follow the evolution of the hyper-cores through time, characterizing the hypergraph structure and its temporal dynamics at different topological scales, and quantifying the multi-scale structural stability of the system. We also define two static hypercoreness centrality measures that provide an overall description of the nodes aggregated structural behaviour. We apply the characterization methods to several data sets, establishing connections between structural properties and specific activities within the systems. Finally, we show how the proposed method can be used as a model-validation tool for synthetic temporal hypergraphs, distinguishing the higher-order structures and dynamics generated by different models from the empirical ones, and thus identifying the essential model mechanisms to reproduce the empirical hypergraph structure and evolution. Our work opens several research directions, from the understanding of dynamic processes on temporal higher-order networks to the design of new models of time-varying hypergraphs.
Key words: Temporal hypergraphs / Hyper-core decomposition / Temporal-topological characterization / Multi-scale structural stability / Model validation
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjds/s13688-024-00490-1.
© The Author(s) 2024
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