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Higher-order shortest paths in hypergraphs
Berné L Nortier1,2, Simon Dobson1, Federico Battiston2
1University of St. Andrews, Department of Computer Science, St. Andrews KY16, Scotland.
Physical Review. E
|December 23, 2025
Summary
This study introduces path size to measure higher-order connectivity in hypergraphs. Nondyadic interactions are vital for system connectivity, while dyadic edges connect peripheral nodes, especially in time-varying systems.
Area of Science:
- Network Science
- Graph Theory
- Data Analysis
Background:
- Complex networks exhibit emergent connectivity from local interactions.
- Hypergraphs model networks with higher-order interactions but their connectivity is understudied.
Purpose of the Study:
- Introduce path size to characterize higher-order connectivity.
- Quantify the relevance of nondyadic ties for efficient shortest paths in empirical networks.
- Analyze networks with and without temporal information.
Main Methods:
- Introduced 'path size' as a novel metric for hypergraph connectivity.
- Analyzed diverse empirical networks, including those with temporal data.
- Compared results against randomized null models.
Main Results:
- Nondyadic ties are often central and vital for overall system connectivity.
- Dyadic edges remain crucial for connecting peripheral nodes.
- This effect is more pronounced in time-varying systems.
Conclusions:
- Nondyadic interactions play a significant role in the connectivity of complex systems.
- Path size offers a valuable tool for understanding hypergraph structures.
- Findings advance the understanding of systems with higher-order interactions.
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