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Summary
This summary is machine-generated.

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.

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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.